As the manager of the away team, Mourinho had expected to be allowed to do his post-match press conference first - as is customary - so that the Premier League champions could make an early start on their journey back to London.
The Portuguese was furious that Martinez elected to speak to the media before him, forcing Mourinho and his players to delay their departure.
As a result, the two-time Champions League winner interrupted Martinez while the Everton boss was speaking with a group of journalists near the pitch.
“Roberto, next time tell me go before you because we have to travel," Mourinho said.
Martinez countered: "We don’t control that, Jose. I don’t control that.” An exasperated Mourinho then exclaimed: "F****** hell!"
After Mourinho had stormed off to attend his press conference, Martinez said: “When he beat us 6-3 [last season], he was such a nice man. I prefer him like that!”
When asked if he would nonetheless invite Mourinho for the traditional post-game drink, the former Wigan manager replied: "Of course – and I am sure he’s going to come round."
Martinez has previously criticised Mourinho over Chelsea's interest in Everton defender John Stones, claiming that the Blues were guilty of unsettling the England international, who had a transfer request rejected before the close of the summer window.