Steve Clarke guided his home nation to their first appearance at a major tournament in 23 years, but tonight's defeat, coupled with another loss in their opening match against the Czech Republic, prevented qualification to the knockout phases for what would be the first time in their history.
Callum McGregor had the nation on its feet with a typically composed effort to cancel out Nikola Vlasic's opener in the first half, but a second period of dominance for Croatia was capped off by goals from stalwarts Luka Modric and Ivan Perisic.
Both sides entered the fray with a point apiece knowing only victory would ensure progression, with Zlatko Dalic's side coming off the better and joining fellow Group D side's England and the Czech Republic in the last 16.
Story of the match
Despite the somewhat perceived decline of the 2018 World Cup finalists' midfield dominance, the need for the same composure in the middle of the park shown against England was paramount going into the must-win game.
Doing so without Man of the Match at Wembley Billy Gilmour, who contracted Covid-19 in the days following the stalemate, required a proactive attitude from the off.
Scotland, just as they had against the Czech Republic last week, got off to a pacy start and had an opportunity to open the scoring in the opening five minutes.
The Tartan Army needed to do something they had not achieved in their previous two games in order to progress- score.
An accumulated 2.61 expected goals (xG) so far in the tournament pre-kick-off shows the Scots' have had opportunities to put it away, with the finishing of Che Adams and Lyndon Dykes leaving a lot to be desired in otherwise positive displays.
The awareness of the aforementioned potency of their opponents' midfield trio was acknowledged at times, were out of possession, Clarke's men could drop deep and manoeuvre their way through the press with the ball.
Scotland's positional awareness was found wanting not long after as Josip Juranović was easily located with time on his hands in the right flank, guiding a cross back into the mixer.
Nikola Vlašić was able to deftly control Ivan Perisic's knockdown at the far post and tuck the ball away while off-balance to the right of David Marshall, adding an extra mile to Scotland's potential rocky ascent to qualification.
The direct incisiveness from their midfield that was previously unfounded in Croatia's first two matches went under a renaissance in the first period, with one of its main architects Luka Modric denied from range by Marshall's fingertips.
An opposing midfield talisman in McGinn wanted to make an impact of his own and had two bites of the cherry to do so; directing a teasing header wide of the target that was just retrieved by Adams, where in the following phase of play the former put his effort wide again with no other man in blue to able to aid in his recovery this time around.
The Croats' threat extended to the left flank in two forms, perhaps in the more established talent of Perisic, scoring in every one of his countries appearances in major tournaments since 2014, and young full-back Joško Gvardiol, posing a danger to Stephen O'Donnell who was not at his imperious best in the first half as he was at Wembley.
Just as Zlatko Dalić's men established possessional superiority, Callum McGregor, known for his composed finishes in the national arena for his club Celtic, netted his first goal in the royal blue of Scotland at a time when his country needed him most.
The deep-lying midfielder was found lurking at the edge of the area, taking a touch with his preferred left and finishing with his weaker right foot to send Hampden into raptures before halftime.
While Marshall's sweeper tendencies were found out against Patrik Schick last week, they saved the day against the marauding Gvardiol, both of whom collided but were able to carry on.
McGinn, Scotland's top goalscorer under Steve Clarke, was in the wars at the other end after having the chance in closest proximity to a goal go begging in literal agonising fashion, with the Aston Villa man being stunned by Livakovic's wayward glove.
Nonetheless, Modric's earlier threat at goal could not be suppressed by Marshall in the second half, his classy finish with the outside of the boot soaring into the top right-hand corner following some cool intricate play involving Bruno Petkovic and Mateo Kovacic for the Checkered Ones.
The final phases were representative of large portions of the game as a whole, as Croatia's second goal condemned Clarke's men to fight back in a relatively subdued Hampden where possession was scarce and chances even less so.
Any hopes of a turnaround were constrained to a singular passing triangle instigated by Scott McTominay, where the final pass frustratingly eluded the youngster.
A pinpoint Luka Modric corner fittingly burst the Scottish bubble after such commanding ninety-plus minutes, as Perisic leapt over Kieran Tierney and met his cross to glance into the far corner, the winger's ninth in major tournaments.
While it could be argued that their services might have been best utilised at different moments of the tournament altogether, substitute appearances from Kevin Nesbit and Callum Patterson were symbolic of the bright future ahead for Steve Clarke.
Man of the Match- Luka Modric
Age seems to be but a number for the former Balon d'Or winner.
Modric, who turns 36 in September, showed the qualities of a captain in his performance and became the oldest player to score for his nation at the Euros with a sublime goal that, while only putting his side a goal ahead, highlighted the gulf between the sides as Croatia remained in control for the game's remainder.
The ever-present midfielder also registered 115 touches of the ball, 86 passes and had 100% successful dribbles in the win, kick-starting an otherwise dormant Croatian showing at the Euros thus far.
Another goal involvement in assisting Perisic's goal and Croatia's third put the final nail in the coffin for Scottish hopes and sealed his own team's qualification to the next round.
Scotland, perhaps regretful with hindsight in not getting more out of the Czech Republic and possibly England games, are safe in the knowledge they were beaten by a much better outfit on Matchday 3, anchored by Modric.