Barkley was only shown a yellow card by referee Anthony Taylor five minutes before half-time after catching Lovren on the ankle with a heavy tackle, one that prompted a vehement reaction from Klopp.
However, the German's post-match comments were far cooler, as he refused to comment in detail on that specific duel.
"I don't like creating stories," Klopp told Sky Sports.
"Our responsibility is to cool things down as much as possible. It's not so easy in the game when we shout at each other.
"If you saw two harsh challenges then say it, don't use me to say it.
"It's the third game we leave with an injured player – Sadio [Mane] was unlucky."
Ronald Koeman criticised Klopp for his reaction to Barkley's tackle and suggested that Lucas Leiva was guilty of excessive force during the match, but Klopp did not share that view of the Brazilian's performance.
"Lucas is a very experienced player and we used him a lot this season at centre-back, but everyone knows he's a six," said Klopp.
"We needed him there [in central midfield] and he did the job. His challenges, he was very aggressive – legal aggressive."
When asked about Koeman's comments in particular, Klopp replied: "Ronald Koeman spoke about me? Then say about it what you want."
The Liverpool manager then promptly walked away.