The Liverpool midfielder was quick to play down the incident following the 1-1 stalemate after Henderson accepted an apology from Barkley after the full-time whistle.
Such a poor tackle then sparked a confrontation involving both sets of players, with Romelu Lukaku seemingly taking exception to the reaction of an irate Dejan Lovren.
Referee Mike Dean gambled with his approach early on at Goodison Park and the game benefited as a result.
"Of course it is [about] character but I was never in doubt about the character - but it was the situation", said Klopp. "Everything is clear. If you saw it say how it was".
"I thought the boys were brilliant. He (Barkley) was lucky - and Hendo was lucky that nothing else happened".
Everton boss Ronald Koeman felt his side did not deserve their defeat as he felt a number of factors went against them. He [the referee] gave Coleman his first yellow card but not a second to Lovren. Why? The referee gave a yellow card to Coleman and not to Lovren, even though he started it. Lovren was already on a yellow. "That's what I don't like".
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"Barkley, maybe he was lucky". Maybe, I don't know. "Maybe it's a red", the Dutchman added.
Jordan Henderson and Ross Barkley remain friends despite the Liverpool captain being caught late by the Everton midfielder on Monday. "But I know Ross well". "He's a good lad and I'm good friends with him".
"He mistimed the tackle and after the game he apologised". Thankfully I'm alright. It was just mistimed, you're going to get them in derby games. It's the best place you can win an away game but it's three points at the end of the day.
Jordan Henderson hailed the spirit and character of his Liverpool teammates after they secured the local bragging rights once more with victory in one of the most dramatic Merseyside derby encounters of recent times.