The Reds were made to work hard by both their opposition and the weather at Anfield, but despite two scares with goals from Ashley Westwood and Johann Berg Gudmondsson, they were able to push for the win.
Victory keeps Liverpool within a point of Man City at the top of the table, and speaking after the game Klopp was positive in his assessment.
“It was good, 4-2 is a brilliant result,” he told reporters.
“We knew it would be difficult against Burnley, it always was for us but most of the time we could win, and we always felt the work.
“That’s how it should be: all good.”
Westwood’s opener came directly from a corner, with Alisson pinned down by James Tarkowski, but Klopp took a sensitive view when questioned on Andre Marriner’s decision to allow the goal to stand.
“The last part of the season is the decisive part of the season, for all of us it’s the same,” he added.
“To win something you always need to have a bit of luck, and that’s involved.
“If Andre Marriner has a better view of the situation he probably would have whistled it—I think, we have to ask him.
“It’s always influential, but it doesn’t help if we now put more pressure on the [referees]. I think they try everything to whistle in the right way.”
Adam Lallana made a rare start in the middle of the park and was named Man of the Match, vindicating Klopp’s faith after an impressive week in training.
“It was clear if he can play like he trained, then he will help us a lot,” the manager explained. “That’s exactly how it happened today.”
And despite failing to score a record 50th league goal for the club, Klopp described Mohamed Salah as “the best player on the pitch,” applauding the Egyptian for his all-round game.
“The message for the day is that nobody gets rid of us if we play as we played today,” he added.
“We had the perfect mixture of fighting the opponent, fighting the circumstances and playing football.”