Jose Mourinho says Jurgen Klopp got the wrong end of the stick when the two managers confronted each other on the touchline at Old Trafford.
Both players were booked after Herrera fouled Firmino, prompting a reactionary shove from the Liverpool forward.
Mourinho revealed Klopp had wrongly thought he was calling for a Liverpool red card prior to the two bosses having to be separated.
"He thought I was asking for his player to be sent off," Mourinho said at his post-match media conference.
"I wasn't, so no problem at all.
"I think the game was correct, I think the players gave everything in an emotional way, professional way.
"I think the referee managed very well that part of the game. So I think the game was a great publicity for the Premier League all around the world."
The match saw Zlatan Ibrahimovic head an equaliser six minutes from time, cancelling out a first-half James Milner penalty that was awarded for handball against Paul Pogba.
Mourinho conceded the decision was probably accurate, but could not resist another dig at some of the officiating his side have received this season.
He added: "I didn't watch but the referee was very close so it probably is a penalty.
"The problem is the criteria. Sometimes you give them. Sometimes you don't. It's amazing that in 21 Premier League matches, three in the League Cup and one in the FA Cup - 25 matches - we had one penalty.
"Even Michael Oliver told me at the end of the game, 'This time it was a penalty!' It looks like it was a penalty.
"We can do, and have done, much better this season in terms of the quality of our game, but I think Liverpool can do better than what they did too.
"As a proper derby it had everything. It's good to see that Liverpool also can play defensively and on the counter-attack they were always dangerous."