Chelsea (67 points), Liverpool and Leicester City (66 points each) are in a three-way battle for the last two Champions League places ahead of Sunday's matches.
Liverpool were eighth in March with Champions League qualification looking unlikely, but Klopp's side went on a nine-match unbeaten run to move up to fourth.
"I can't remember a season when we didn't go to the wire. I'm used to stress until the last match day," Klopp told reporters ahead of their home game against Crystal Palace.
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We've found some stability and created confidence again. We've scored in the right moments and conceded fewer.
"That's what we had to do. But (in) these kind of games, anything can happen. Nobody should expect the perfect game, I respect Palace too much."
Liverpool beat Palace 7-0 in the reverse fixture in December which has helped Klopp's side maintain a healthier goal difference compared to Leicester.
However, Klopp said that result was irrelevant ahead of a "really intense game" at Anfield and hoped the 10,000 fans returning to the stadium would give them a boost.
"You can't imagine how much I'm looking forward to seeing 10,000 fans inside Anfield. It's important that we don't lose patience after one minute, we need the best support," Klopp added.
Nothing was the same (without fans), we needed to get used to it and we did, but it shouldn't be like this. It makes a difference. We all need support in life, football is a game based on emotion and we were alone.
Liverpool midfielder Georginio Wijnaldum's contract ends this season and though Klopp said he had no update on a possible extension, he did not question the Dutchman's commitment.
"Gini's character is without question, a sensational guy, completely committed to the club and the team until the last day," Klopp said.
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