Joe Ledley's strike and James Milner's red card seemed to have resigned the Reds to defeat until the 78th minute, when Roberto Firmino capitalised upon an Alex McCarthy error to equalise.
With Alberto Moreno going close before McCarthy produced good saves to twice deny second-half substitute Benteke, the Belgian won a controversial penalty late into stoppage-time - which he stepped up to himself, rolling the ball to the opposite side of the goalkeeper for all three points.
Reds have bounced back from cup final defeat
Lallana, speaking to the Liverpool Echo after the triumph at Selhurst Park, insisted that it was evidence of Klopp's side having developed a "never-say-die attitude" under the manager.
"We stuck at it and showed character," explained the England international, who admitted that it was "strange" after going down to 10 because it "almost took the reins off" he and his teammates, who he believes "played with a bit more freedom and confidence" after Milner's dismissal.
Lallana added that Philippe Coutinho was "brilliant" after coming on and gave the team "that extra bit of quality" that the team needed to get "back in the game", insisting that it helped them to be "outstanding" in the last 20 minutes of the game.
It was Liverpool's third successive league win, and their first against the Eagles in South London since 1997, as they continued on their pathway of revenge.
Having earned a modicum of retribution by beating Manchester City 3-0 in the Barclays Premier League just days after losing against them in the final of the Capital One Cup final, the Reds ended a three-match losing streak against Palace.
Lallana hailed the reaction that Klopp and co. have produced since the disappointment of losing the final at Wembley.
"It's been a big response," continued the 27-year-old, who said that the team "all felt so disappointed" after losing out on penalties against City.
But he said that the team "needed to put it behind" themselves, revealing that they said before the game at Selhurst that victory would be "even bigger than beating Man City on Wednesday night."
Lallana said that "to win in the last minute says a lot about this team" having suffered some "bad defeats" at the hands of Palace, at both Anfield and on the London club's patch, insisting that they "owed them one" as a result.
Ice-cool Benteke can use winner as a springboard
It was summer signing Benteke, who has endured a tough few months outside of the starting eleven, who helped Liverpool to come away with a morale-boosting win.
Netting his first goal of 2016, and his first in 14 games in all competitions, Benteke earned high praise from the Reds' No.20 - who said that he showed admirable nerve to win it so late.
"I was delighted for Christian," declared Lallana, who said he's been "working extremely hard" to fight his way back into the team.
Calling him "a top striker", Lallana said that he's "proved himself in the Premier League" despite having gone through a barren spell.
"He showed great composure to score after being brought down for the penalty," he continued, saying that it was "ice-cool" in the matter he despatched the spot-kick.
According to Lallana, Benteke's last-gasp winner will serve as "a massive moment" for both the striker and the team, who can "push on from this now."
Attentions now turn to a mouthwatering Europa League last 16 first-leg with Manchester United on Merseyside as the two teams do battle in Europe for the first time ever, and Lallana says the Reds are looking forward to it.
He acknowledged that it's "going to be massive" over the two legs, saying that Anfield will be "rocking" on Thursday night which can help the team "get a lead to take into the second-leg at Old Trafford."