Alan Pardew suggested the lengthy delays on a cold night at Anfield had contributed to Hal Robson-Kanu and Kieran Gibbs suffering muscle injuries, while Jonny Evans and Jake Livermore also appeared to be struggling in the closing stages.
VAR was used to award a penalty for a foul on Mohamed Salah, while referee Craig Pawson disallowed a header by Craig Dawson after consulting replays.
Klopp called for patience in the adoption of the new technology, although he believed Ahmed Hegazi could have been sent off for a challenge on Roberto Firmino.
"I think it is normal. Of course it will change things," Klopp told reporters after his side's 3-2 loss.
"Is it nice that West Brom celebrates a goal and then somebody tells them it’s not a goal? But I think it's important, that's actually what we always wanted – that if a goal should be disallowed, it should be disallowed.
"Usually in these two situations after the game we talk about it and I have to explain a defeat which maybe wasn't deserved because we didn't get a penalty and they scored another goal.
"It's normal in the beginning that it takes a little bit longer, is it cool in January when it's cold for the players especially, probably not. That will, I think, become a little bit smoother, a little bit more fluent in the future.
"But in the end, you ask me about it and I've said it already in plenty of interviews that if we have a video assistant ref then Mr Hegazi was really lucky tonight that he ended the game on the pitch, it was a harsh, harsh, harsh challenge and if you have VAR and we talk about the game like a situation like that, then that's obvious.
"I think it was not even a foul, that's then of course strange, for sure not right, but that was not the reason we lost the game."
Liverpool saw an 18-match unbeaten run in all competitions ended by Premier League bottom club Swansea City on Monday, while defeat to the Baggies was their first loss at Anfield since April.
And Klopp is now targeting a new undefeated sequence, with the Reds next in action at Huddersfield Town in the league on Tuesday.
"Yes, that would be a good idea," Klopp said. "Look, it's not the first game I've lost, it's not the first game I've wanted to win really desperately and I lost it.
"But it's deserved, for me, for the boys, it's deserved. I thought the crowd did really, really well. Obviously they remembered better the good performances here than we did and at the end they appreciated that we at least tried to sort our problems.
"That's the job to do, you cannot go out there and be completely without a plan or an idea, you have to show up in a game like this, you need to be ready still, even if you make three big, big, big mistakes in the first half.
"You need to be ready to make mistakes again, but in an ideal world not in and around your own box. So yes, we should try but first we have to really think about what happened tonight and make ourselves ready for Huddersfield. A long run starts with the first game and that's on Tuesday."