The Spaniard was forced off in the 45th minute of the game after turning his ankle and was in tears as he was replaced by James Milner.
Moreno has improved significantly this season, becoming a key part of Liverpool's first-choice line-up.
The injury makes him a doubt for Sunday's Merseyside derby, with Klopp admitting that it took the shine off an otherwise very successful night for 'The Reds'.
"We had a little shadow on the night when Alberto Moreno needed to get substituted. It was a strange situation," said Klopp following the game.
"He is a tough guy and if he cannot continue the game then you should consider it could be something serious.
"In the treatment room then, he was a little bit more positive, so maybe we are lucky and it's not too serious. We will see.
"We need all the boys, we need all the boys for the next few weeks, but especially in this week for the next game on Sunday."
The German felt that the game showed that Liverpool have learned from the mistakes that saw them throw away a three-goal lead last time out in the Champions League.
"We showed tonight that we learned from the mistakes we made in Sevilla - now we have to show we have learned from the mistakes after Maribor when we faced Tottenham," he explained.
"We will be ready again on Sunday and if the crowd is ready to help us it would be nice again."