Mignolet was still named in the matchday 18 but Klopp opted to use understudy Karius from the start as Liverpool took on Alan Pardew's Baggies.
"Si got a little knock in the last game, swollen around the ankle," said Klopp, according to the official Liverpool website.
"If you don't have another goalkeeper, Si could have played, but there's Loris. So I think it makes sense that we make the change and hopefully we don't have to make a change during the game.
"Si did OK today in training, absolutely, but we only had a little session. Yesterday, he couldn't train. So, that's the reason for that."
Klopp started with Liverpool's so-called Fab Four, Philippe Coutinho, Sadio Mane, Mohamed Salah and Roberto Firmino, but it was not enough to break down a stubborn West Brom side as the Merseysiders missed the chance to go back into the top four.
Hal Robson-Kanu struck the bar in the first half as Liverpool became increasingly frustrated while Karius had to be at his best to keep out Jonny Evans' header. Ahmed Hegazi could well have won it himself but headed over from point-blank range.
Liverpool thought they had won it at the death when Joe Gomez's cross was turned in by Dominic Solanke but referee Paul Tierney spotted a handball by the England youngster and the goal was disallowed, to leave Klopp visibly angry at full-time.
"The disallowed goal was harsh," Klopp told reporters. "Solanke 100% used his chest, it is how it is. We had good chances in a stiff first half, we changed the system a few times to try and get in the right positions, but we didn't play our best football.
"We were a little bit stiff, we were not at our best today - we needed a bit of luck - three minutes extra time at the end of the game is a little harsh as well!
"If feels not too good, but it is our responsibility - we have to play better football because we can play better football.
"We have to carry on, that is how it is. It was not our best game but we have to go again - we had chances to win. Rondon did really well for West Brom, he worked really hard.
"What can I say? It is one point more, but it is not what we wanted - that is how it is."
The result keeps Liverpool fifth in between north London rivals Tottenham Hotspur and Arsenal locked on 31 points with only goal difference separating the trio. They travel to AFC Bournemouth on Sunday [17 December] in their next league outing.