Klopp's side became the first side to stop Leicester scoring in the league this season as Claudio Ranieri's team were beaten 1-0 at Anfield on Saturday -- their first defeat since September.
That was Liverpool's first win in five games and they go to Sunderland on Wednesday on the back of successive away defeats in the Premier League.
Reds boss Klopp therefore insists his side has no right to take anything for granted, despite Sunderland's position in the relegation zone and their chastening 4-1 defeat at Manchester City in their last game.
"There's no doubt about the quality of the players, the character. What we have to create is a stable level of performance," Klopp said.
"We have to go to Sunderland and be concentrated from the first second, like we were against Leicester.
"We want to win at Sunderland. That's the only reason why we travel there.
"We have no doubt as to the mentality of the team. Nobody in the team thinks 'it's only Sunderland'.
"We want to develop and get more points in these very important moments in the league."
Klopp expects a strong Sunderland reaction to their defeat at City as the Wearsiders scrap for survival and will prepare his players for a physical battle.
"I think second balls will be a big thing to think about for Sunderland. They will go back to their roots. We know what is waiting for us."
Liverpool will not rush back striker Daniel Sturridge, who has returned to training following his latest four-match injury absence with a hamstring strain, and are awaiting the results of a scan on a hamstring injury Divock Origi sustained against Leicester.
Winger Jordon Ibe could return following illness, but defender Martin Skrtel and midfielder James Milner, who is due to return to training on Tuesday, are still missing.
- Shattered -
Meanwhile, Sunderland boss Sam Allardyce admits he is taking a risk by turning to veteran defender Wes Brown against Liverpool.
Former England international Brown is set for only his second appearance since May, with his most recent coming in last month's 6-2 defeat at Everton.
The 36-year-old is on standby to replace former Manchester United team-mate John O'Shea, who is struggling with a calf problem picked up in the City defeat that left the Black Cats second-bottom.
With Younes Kaboul facing up to two months out with a torn hamstring, Allardyce is short on options for the Liverpool clash.
He is ready to shift his formation to protect Brown, and said: "I could have covered any injury, apart from one to John O'Shea.
"We have Wes but he hasn't played much football at all this season so that would be a bit of a concern. But that will be the case if John doesn't make it.
"We'd have to play a different way and play a certain system to use Wes' experience and also give him a little bit of protection.
"We know that he's getting a little bit older and he's not quite as quick as he used to be."
Following an upturn in results after Allardyce took charge in October, Sunderland have lost their last four games to leave them five points adrift of safety ahead of the latest round of fixtures going into their final game of 2015.
"We had some positive results when I arrived and I thought that would lift the confidence," Allardyce said.
"But all of a sudden, that confidence is shattered again. I see a lot of fear back in the team and I have to use my experience to dispel that.
"I need to put the players in a good frame of mind so that they go out and fight their way out of this."