Georginio Wijnaldum's opener just before the hour and James Milner's penalty secured a ninth consecutive win in all competitions for Klopp's men and moved them two points ahead of Manchester City, who have a game in hand, at the top of the table.
"It's really massive. We spoke a lot about this game, how special it is, how special the situation is for the opponent," said Klopp, who bemoaned the dry state of Cardiff's pitch under baking temperatures.
"It was not a game for playing around. It was a battle of will, who wants it more."
City travel to Manchester United on Wednesday in what appears the toughest hurdle left for the English champions to clear and deny Liverpool a first Premier League title in 29 years.
The Reds remain poised to pounce if Pep Guardiola's side fail to pick up maximum points in their remaining four games.
However, unlike when Liverpool visited Old Trafford in a 0-0 draw early in Ole Gunnar Solskjaer's caretaker reign in charge, City look to be catching United at the right time as the Red Devils were thrashed 4-0 by Everton on Sunday.
"Man Utd was in a much better moment when we played them," added Klopp. "But even if United gets a point or something, we still have to play games after that. We just have to stay focused on our things."
While Liverpool were cruising into a second successive Champions League semi-final in midweek, Cardiff gave their chances of survival a huge boost with a 2-0 win at Brighton to close within three points of safety.
If Neil Warnock's men are to defy the odds to stay up, it is upcoming games against already relegated Fulham and Crystal Palace they will need to win, but they did not make life easy for Liverpool.
"There is not a weakenss in them," said Warnock. "They are miles ahead of anybody these two teams (Liverpool and City)."
"I'm just glad we don't have to play either of them again."
The visitors should have taken the lead midway through the first-half when their front three clicked together for the first time as Mohamed Salah fed Sadio Mane and the Senegalese's pass put Roberto Firmino clean through on goal. However, the Brazilian blazed over with just Neil Etheridge to beat.
Salah has found his form in front of goal at the right time for Liverpool's bid for a Premier League and Champions League double.
However, after scoring in three of his past four games, Salah could not keep that streak going as he fired too close to Etheridge when played in by Jordan Henderson.
There was little reason for Liverpool to panic at half-time as their previous four Premier League games had also been won with second-half goals and so it proved once more.
Trent Alexander-Arnold bagged his 10th assist of the season as the England international's corner was pulled back for Wijnaldum to lash into the net first time in a routine Klopp revealed was crafted by the players at half-time.
A corner at the other end should have brought Cardiff level when Sean Morrison seemed to have the simple task of nodding into an empty net as Alisson got caught underneath a corner, but he mistimed his header and the ball instead bounced to safety off his back.
And Morrison was the Cardiff villain once when he was adjudged to have brought down Salah inside the area, even if the Egyptian's fall to the floor was theatrical.
"The last bit was a great 9.9 dive, wasn't it," argued Warnock.
Milner did not care as he confidently dispatched the spot-kick to keep the pressure up on City.