Having led through Jordan Henderson's well-worked goal the Reds fell behind after Craig Dawson and Jonas Olsson - who also had a goal ruled out for offside - both converted two corners only for substitute Divock Origi's deflected long-range strike in the sixth of eight added minutes to rescue a point.
The lengthy additional time was for the long delay after Craig Gardner's reckless knee-high challenge - which went unpunished - on Dejan Lovren saw the Croatia defender carried off on a stretcher.
At various times during the match there were words exchanged with West Brom counterpart Tony Pulis and at the final whistle there was no handshake as Klopp raced to celebrate with his players, although he was confronted by a member of the visitors' backroom staff.
Klopp led his players to the Kop to thank them for their support and admits he enjoyed the draw more than he should have.
"It was the best atmosphere since I've been here, I enjoyed the atmosphere with my whole body. I want to say 'thank you'," he said.
"Sometimes a point deserved in the right way is more important.
"I know three points is important for the table but for development - the style of play against a team like this; everyone tells us we can't play against teams like this but yes we can; staying in the game - to come back, that is a big moment in football.
"On Thursday (against Sion in Switzerland) we played on ice; today against a wall and it was not easy to create chances against a team like this.
"Maybe the crowd were disappointed but they didn't let us feel that. We were all in the game. We all wanted this one point and it felt like three, in this moment it was an explosion."
Klopp refused to criticise Gardner for his challenge or expand on his disagreement with Pulis.
"He (Gardner) played the ball, a millisecond before he hit Dejan," he added.
"It was like the whole game, on the edge of everything. I am not sure the ref saw it.
"We hope it (Lovren's injury) is not too serious but we have to wait for the scan.
"Everything could have happened in this situation but hopefully we'll have more luck than in previous situations (with injured players)."
On Pulis he said: "I didn't see him after the game. I can say nothing. We had some words in the game; sometimes it takes more than a few seconds to cool down.
"Usually I shake hands, I did not today because it was not a friendly game."
Klopp also defended goalkeeper Simon Mignolet, who continues to draw criticism.
"I said to Simon at half-time, if somebody says it was your fault, it is not true, it is my fault. I have nothing negative to say about Simon," he added.
"They had six or seven players who were six foot four or taller and that is really difficult to defend but we will do better and work on it.
"In England it is really difficult for goalkeepers to come out as there is no-one to protect them but he can help if he comes out."
Source: PA