Sadio Mane and Philippe Coutinho gave the Reds a comfortable 2-0 lead at the break, which could have easily been extended if they had not spurned good opportunities before Gareth McAuley pulled one back late on to cause some concern.
But the hosts held on to continue their run of 11 games unbeaten at their Anfield home and go level on points with Arsenal at the top of the table, and Klopp paid tribute to the fans.
He told BT Sport: “I’ve been here a little more than a year, but that was the best performance of the crowd in a non-European game.
“The atmosphere was outstanding, it was Anfield at its best. I was really, really happy [with] how the crowd respected West Brom and how they know it’s a difficult game.”
On his team’s performance, Klopp said: “Who needs clean sheets when you get three points? The lads did outstanding and I’m really pleased with the performance.
“It’s unbelievably difficult against West Brom because so many balls are in the air and you always have to concentrate—their set-pieces are so dangerous.
“But I think it would have been a joke today if we drew the game or didn’t win—our performance was really good against a team like this.”
Baggies boss Tony Pulis believes Liverpool are genuine title contenders.
He told BT Sport: “They are a terrific side, the players they have got and players on the bench that they can bring in, they have a clear run at this title this year.
“If you look at the clubs that play in Europe and have to play tomorrow, this football club has a real chance this year.
“We wanted to push players on further forward, but it’s difficult when 2-0 down against a good team like this.”