The last meeting between the clubs brought a frustrated post-match response from Klopp, angered by goalkeeper Fraser Forster's antics after he approached penalty-taker James Milner and wrecked the spot with his studs before saving his compatriot's spot-kick.
In fact the Reds were unable to score against Forster in 360 minutes last season, producing goalless draws in both of their Premier League contests and losing both legs of a League Cup semi-final 1-0.
But the South Coast club have since undergone a change of management with Claude Puel sacked in June and former Liverpool defender and first-team coach Mauricio Pellegrino appointed his successor.
And Klopp therefore believes nothing can be taken from their clashes last season as they go looking for a first win over Southampton since December 2015.
Reds boss calls upon charges to "strike back"
Klopp insisted that last season's contests with Southampton "were all different games" and therefore won't be used for their analysis of this coming clash "because Southampton's team has changed."
"I don't care how long it's been since we scored," Klopp retorted when told Liverpool have gone four games - and 428 minutes - since last scoring against the Saints.
He added: "I know it will be difficult again to win against Southampton, but it's still possible. It's obviously not a friendly game because there is a special relationship between Southampton and Liverpool – we have given them a lot of money for a few players."
The German believes the Merseyside outfit have "always paid a fair price" in their dealings and moved on to their last meeting, reflecting on "the situation around the penalty."
The Reds boss felt it "looked really strange and not particularly fair" and insisted: "I don't forget the last game with a very decisive situation for us."
He noted that Southampton - well clear of danger and without the possibility of European qualification - "didn't need the points" but that "it felt like somebody created stories so that they were really spurred on, like Forster with the penalty."
Klopp vowed: "I think it’s a good moment to strike back."
Klopp impressed by Southampton's possession-based approach
Liverpool have scored 10 goals in their last three games since a humbling defeat at Tottenham Hotspur, having appeared to turn a corner with three wins in three.
Only their most recent win, a 4-1 thrashing of West Ham United away from home, really showcased the dynamism and effervescence of their attack but Klopp is more wary about being well organised defensively.
Commenting on his side's recent run of form, he insisted their improved streak of results "doesn't mean we are going to score four again."
"What we knew before and what we know now is that we have to improve defensively," acknowledged Klopp, saying that Liverpool must protect themselves better as they "did in those three games."
He praised how his side didn't offer their opponents "a lot [of opportunities] on the counter-attack" and called that "very important for a dominant side" in a game.
Klopp warned that Liverpool must do so again but also said that Southampton are "a different team" and calling it "quite impressive" that they are "fourth in the table for possession" of the 20 top-flight teams.
Although Pellegrino's side "haven't got too many points so far", Klopp added, he insisted that they "probably still feel good in their situation and feel confident" and told his players: "It's our job to make them feel less confident during the game."
Klopp brushes off van Dijk questions
The clash with the Saints will also see Virgil van Dijk play at Anfield for the first time since a messy transfer saga engulfed the summer transfer window, though not in a Liverpool shirt.
Asked about the club's lengthy failed pursuit of the Dutch defender, Klopp joked to a reporter: "You really expect an answer? There is nothing to say on that. Absolutely."
On whether he hopes his Liverpool side ensure van Dijk - who could yet still join the club in the future - has a busy afternoon, he said: "Hopefully. It should be difficult for every player to come to Liverpool. Hopefully it is a difficult time [for him]."