The Belgium international, who scored the only goal against Leicester on Boxing Day, did it again at the Stadium of Light when he took advantage of some flat-footed defending 22 seconds into the second-half to clinch a 1-0 victory for his side.
Klopp said: "We were the better team and you could see that the pressure on both teams was big.
"The pressure was on a little bit more for Sunderland because of the intensity of the last weeks and months. You could help yourself if you got an early goal. We didn't but we did not do too bad in situations against a very good defensive team.
"They were only defending so that makes it pretty hard for us because you don't get space and you always have to go again and slow down the game.
"Then we created the goal after half-time and we controlled the game. They were waiting for set-plays, they are difficult to defend against but we did it.
"We could have got a second or third goal, we didn't, we had to wait until the final whistle."
The Reds are now level on 30 points with sixth-placed Manchester United, but the Black Cats are seven points shy of safety at the halfway stage.
Sunderland boss Sam Allardyce felt his side were unfortunate in the manner that Liverpool got their goal but praised his men's effort, although he conceded a lack of killer instinct in the final third.
"We didn't really produce enough quality," he said.
"When we did we got good chances, we couldn't finish them off but we could have done more with the opportunities in terms of our final third quality - we need to try and get that a little better.
"A resilient performance, one where Liverpool never really looked like creating too many clear-cut chances or opportunities and if we can build on that scenario and get a bit more luck then we'll try to go up the other end, get a result and score a goal.
"The injuries are a problem. We're facing another centre-half who's come off injured so we'll have to wait and see how Seb (Coates) is. I thought Wes (Brown) did great. I thought the team did well overall, a good shape to the side.
"They're playing a Liverpool side that's got a huge amount of money spent on it and often matched them."
Sunderland have taken just two points from their past seven Premier League meetings with Liverpool.
And the Black Cats are now on their worst run of Premier League defeats - five in a row - since April 2014.
Liverpool have won five games 1-0 this season, a Premier League joint-high along with West Brom.
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