Jose Mourinho responded to Antonio Conte's apparent handshake snub following Manchester United's 1-0 defeat at Chelsea on Sunday by saying that congratulating Conte's assistant had been enough.
Conte appeared to choose to celebrate with his players on the pitch after the final whistle at Stamford Bridge rather than shake Mourinho's hand.
And the United manager told reporters: "You want me to go and chase him in the middle of the pitch? I was there.
"I shook hands with the people who were there. I think one of them was his brother, the assistant, so I feel that, by shaking the hands of his brother and the other assistants, I did my duty.
"I cannot go and run to chase him."
Mourinho also said he was "worried" about Manchester City's lead in the title race but maintained that United could make up ground when Paul Pogba and Zlatan Ibrahimovic return from injury.
City beat Arsenal 3-1 earlier in the day to leave them eight points clear of United at the top of the table.
Mourinho said: "We are worried, but there are 18 teams more worried than us because we are second.
"Eight points in the Premier League is not the same as eight points in the Portuguese league, La Liga, the Bundesliga.
"Eight points in the Premier League... there's still a lot to play for.
"I hope, I feel, I think, I wish that in the busy period of late November, December, beginning of January, probably we are going to be at our maximum strength with Pogba, Rojo and Ibra back, so probably we can be on a high."
Alvaro Morata scored the decisive goal in the second half at Stamford Bridge, and Mourinho's United have now scored only one goal in seven games away from home against the top six.
They had chances through Marcus Rashford, Romelu Lukaku and Marouane Fellaini, and Mourinho said he felt a draw would have been a fair result.
He added: "The team that scored first probably would win, because both teams are very good defensively.
"Being in front will always be an advantage. But they scored before us, and then they were in a more comfortable position.
"But I think we lost emotionally a few minutes after the goal. For a few minutes we were in trouble to be confident again and to try and play again.
"But then we had a good reaction, a good control. They had space to counter-attack, but we had initiative, courage, dynamism and the chances to equalise, which would have been a fair result.
"But this is not about what I think it is, or whether it's fair or not. One goal, three points -- congratulations."