The Liverpool Echo says Unsworth was left fuming on Monday night after Arsenal's players and management failed to apologise following a tackle that saw Welsh international Jones stretchered off receiving oxygen.
Everton defeated the Gunners 4-2 in a game that included a dismissal, a penalty, an own-goal and Jones' horrific injury.
Unsworth clashed with his opposite number Steve Gatting in the aftermath of the tackle, saying to the Arsenal boss “Why don't you just shut up?"
“I thought the tackle was naughty, I thought it was wrong," said U23s coach Unsworth.
“When you see one of your players taking oxygen in a potential broken leg it hurts.
“The referee didn't even give the foul and their player didn't even come over to apologise so I thought that was wrong. It's never an easy moment when you see one of your players carried off with a suspected broken leg."