They went into the break level on terms with the Gunners after Philippe Coutinho's marvellous long-range free-kick had cancelled out Theo Walcott's opening goal.
Arsenal responded with goals of their own through Alex Oxlade-Chamberlain and Calum Chambers, but couldn't find a crucial fourth as Liverpool ensured a winning start to the new Premier League campaign.
Englishman delighted with opening win
"It was very entertaining," Lallana said to Sky Sports after the full-time whistle, despite admitting the visitors "started the game not so brightly" having thought they had "quite a good pre-season" going into it.
He insisted that it is "always difficult" to go to the Emirates Stadium, with this just Liverpool's second win there in 16 attempts, but praised the "bit of magic" that Coutinho conjured up which he said gave the whole Liverpool team "a little bit of a lift" on the stroke of half-time.
On Jürgen Klopp's instructions at the break, and the impact his words had, Lallana revealed he had "a few words" for them and added: "I think we came out brilliantly. We got a bit complacent but we saw it out at the end."
The England international called their opponents Arsenal "a top team" and acknowleged that they themselves have got "a few new players" in the squad who he says are "still gelling together."
However, the 28-year-old says the squad "want to achieve something special this year" after "a great three points", though he knows they "have to be more disciplined as a unit."
Midfielder pleased with Reds' response after half-time
Lallana, on what went wrong in a first-half in which Liverpool were fortunate to come away level after being largely dominated and creating few opportunities, he accepted that "maybe we showed them too much respect."
He said how Klopp "wanted us to get up to the ball more" with "more pressing" and "more counter-pressing" and continued: "We came out of the traps flying in the second-half and got the second, third and fourth [goals]."
The Reds No.20 rued that the away side "let them come back in it" and admitted it was "a bit of a tense last 10 minutes" on the bench after being brought off, but said it was "nice to see the final whistle" and "get the three points" in order to "go home happy."
"We've got confidence and belief" says Lallana
Lallana was asked to describe the platform that gives Liverpool for the season ahead and he revealed the "huge belief" within the ranks under Klopp, suggesting what they are capable of doing by saying: "You only have to look at our squad."
He acknowledged the "top players" on the bench and those also "back at Melwood that weren't fit enough to play" on Sunday afternoon, insisting that they have got "a great squad" overall.
The midfielder indicated that because Liverpool are "not in Europe" then they will have "a lot of weeks" where they "only have to play one game" and will be less fatigued.
"We've got confidence and belief in ourselves," continued Lallana, who added that they will now "take it game-by-game, one step at a team" after a "brilliant" three points in the capital.