Jose Mourinho was involved in a tunnel row with Feyenoord coach Arne Slot following Roma's Europa League victory over the Dutch side on Thursday.
Feyenoord went into the game with a 1-0 advantage from the first leg but Roma went through to the semifinals of the competition after a dramatic 4-1 win at the Stadio Olimpico in the second leg.
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Following the final whistle, a video in the tunnel showed Mourinho shouting "respect" on several occasions as Slot made his way back to the dressing room.
One of Roma's coaching staff members is also heard saying: "If this is how you play, you should go home quickly."
The footage also shows Mourinho yelling: "You look at Napoli and Manchester City, but you should be watching us!"
Before the tie, Slot told a news conference that he preferred the playing styles of Napoli and City compared to Mourinho's tactics.
There was tension during Thursday's game after Roma's assistant manager Salvatore Foti was sent off in the first half for appearing to strike Santiago Gimenez.
Mourinho was full of praise for his team after reaching his second European semifinal in a row with Roma, following last season's Conference League title.
"Maybe someone thinks differently, but in my view, the team played very well in a difficult match to deal with," he told Sky Sport Italia.
"I'm sure the fans would have gone home happy for the team regardless of the result. We have limits, but this team is a family."
Roma will meet Bayer Leverkusen in the semifinals on May 11 and 18 and could meet Sevilla or Juventus in the final.
Information from Reuters was included in this report.