The Reds would have leapfrogged Arsenal on goals scored had they held on to a two-goal lead but had to make do with a 2-1 win after Gareth McAuley exposed their set-piece weakness in the 82nd minute.
Earlier, a wonderful first-half display had yielded goals from the superb duo of Philippe Coutinho and Sadio Mane, setting Liverpool up for an apparent stroll to the summit.
And while Klopp would have been pleased with that, he was just as happy to take the win in less comfortable, but more excitable, circumstances.
“‘Who needs clean sheets when you get three points?” Klopp told BT Sport.
“The atmosphere was outstanding, it was Anfield at its best. I’ve been here a little more than a year, but that was the best performance of the crowd in a non-European game.”
Speaking at his post-match press conference, he added:
“Yes, in dreamland then you win always 4-0, 5-0 and the crowd can go earlier and people can go and do something more serious.
“But this game tonight created one of the best atmospheres because it was exciting towards the end. We created the chances and we didn’t use the chances. In this moment it is better we won 2-1 than 3-0 or 4-0, but all good.
“We have 20 points. It was not possible we get more tonight.”
When it was pointed out that 2-0 would have seen Liverpool wake up on Sunday morning as league leaders, the German joked: “Who wants to be top in October?”
On a more serious note for would-be title challengers, McAuley’s close-range finish ruined what would have been a second clean sheet in a row.
Liverpool’s vulnerability from corners is becoming a pattern and Klopp conceded it was an area the Baggies excelled in.
“The plan was to avoid set-pieces. They are so effective, they really are role models off set-pieces,” he said.
“It felt like there were 15 West Brom players in the box.
“(I have) absolutely no problem with the goal we conceded tonight. I would like to have it that nobody can score against us but first we have to have it that nobody can create chances.”