The FA has already decided not to take any action against Lukaku for violent conduct but Lovren has hit out at the Belgian.
The Belgium worldwide was not punished by referee Martin Atkinson at the time and it was confirmed on Monday will face no retrospective action from the video review panel despite Lovren claiming his foot had connected with his cheekbone.
"He was over me, he could have moved away. To be honest, my point of view is that he did on goal", he told a press conference ahead of the Reds' clash with Maribor in the Champions League.
"But, to be honest, my honest view was he did it on objective".
"Normally you would apologise after that, but I saw that he was nervous during the game". I can not say I'm disappointed, but it is what it is and we need to move on.More news: Iraq, Iran, US "raise" oil prices
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The FA will take no further action against the Manchester United forward, while Lovren insists the incident is now in the past. I can not say I'm disappointed, but it is what it is and we need to move on.
"I know everybody is thinking ahead of a game like this that this is the place where you should rotate or whatever", Klopp told a news conference.
"Now I am in a team who want to win against big teams so I think the situation will change".
Manchester United are now in second place in the Premier League table, and two points behind leaders Manchester City.
Lovren added: "I am fit now". "I had issues with my back and with my groin a couple of weeks ago".
The draw meant Liverpool have only won one of their last eight games in all competitions, including the Champions League, in which they drew their opening group games against Sevilla and Spartak Moscow. "I was struggling but now I am fit".