(REUTERS) - Chelsea manager Jose Mourinho should have apologised to former team doctor Eva Carneiro for his criticism of her, Football Association chairman Greg Dyke has said.

Mourinho accused Carneiro and Jon Fearn, the Chelsea physiotherapist, of being "impulsive and naive" and failing to "understand the game" when they entered the field to treat Eden Hazard during the 2-2 draw with Swansea City on the opening day of the Premier League season.

The FA began an investigation after a member of the public complained about Mourinho's language towards Carneiro during the game on Aug 8.

The FA cleared him of making discriminatory comments to Carneiro, who has left the club. But Dyke said in a letter to FA Council members that the Portuguese was in the wrong.

"I don't think Mr Mourinho comes well out of the whole saga - he clearly made a mistake in the heat of a game, and should have said so and apologised," he said.

"Instead, he has said very little and Miss Carneiro has lost her job.

"Our regulatory team have investigated this and while Mr Mourinho has breached no rules, it was clearly a failure of his personal judgement and public behaviour," the chairman added.