Liverpool comfortably defeated Everton 3-1 on Saturday (1 April) with goals from Sadio Mane, Philippe Coutinho and Divock Origi boosting their chances of cementing a top four position.
However, the scoreline could have been worse for Ronald Koeman's side as Barkley was extremely lucky not to be sent off for a stud up challenge on Lovren in the first half.
The Everton midfielder landed his foot on Lovren's shin after losing control of the ball but got away with a yellow card instead.
"That is the only thing I do not like," Lovren said, as quoted on Sky Sports. "If you make a hard challenge then be open about it and say sorry or something like that."
"Don't talk to the referee and say it was not a foul. I think everyone saw it, especially me, but now it is over. If I show you [my leg] it will be headlines tomorrow."
Following their derby win, Liverpool are now third and while their record against the top teams this season has been solid, Jurgen Klopp's side have faltered against the smaller sides. With Bournemouth visiting Anfield next, Lovren says Liverpool must remain focused.
"We are still there in the top four, but we want to be there at the end to go to the Champions League, so need as many points as possible," the Croatian added.
"There are still a lot of games ahead of us and we must think of the next game. We lost away at Bournemouth, which was a wake-up call for next time, so now we must continue."
"We need to show our qualities in our mind and repeat it against Bournemouth and take as many points as possible. If you want to play in the Champions League then you need to play like a Champions League team."