"It was a week where Manchester City played at home three matches, and we play three matches away", said Mourinho after the game.
"What is important is that we are consistent, that we play most of the time good, and always I see many things that we can improve".
Guardiola and Mourinho were on the touchline at the start, but the latter retreated, taking a seat between coaches Michael Carrick and Kieran McKenna, as he jotted down notes following the opener.
"But, of course I prefer the three points today than the record".
City remain unbeaten 12 games into the Premier League campaign after another impressive display.
The distance between the two teams is already 12 points, an insurmountable obstacle for the Red Devils, and we are only in mid-November.
There was something of a response at 2-0 when Anthony Martial converted a penalty but the hosts ensured there was no danger of that turning into a 3-2 win for the away side, as it had done here in April. We made mistakes, we were punished for these mistakes.
Mo Salah, with his eighth goal of the season, and Xherdan Shaqiri sealed victory for Juergen Klopp's Liverpool side over the league's bottom team, keeping them in touch with City.
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Jose Mourinho: Manchester United are in a top-four battle
We arrive in different circumstances. 'One of the things that broke our plan a lot was the fact Fellaini had to start the game. It is one thing to go to Juventus and play against one of the best teams in the world for 90 minutes.
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United also lost Paul Pogba's presence in the derby after he played through the pain barrier against his old club in midweek and was not fit to feature at the Etihad.
A one-two between Riyad Mahrez and Sergio Aguero saw the Argentina striker produce a fierce shot that David de Gea could not keep out in the United goal.
Ilkay Gundogan finished it off, but the move had taken 42 passes to construct, using every area of the pitch.
"We were in a fight to try to get the equalizer", Mourinho said. "Four points from Chelsea".
Liverpool beat Fulham earlier in the day at Anfield and Chelsea drew 0-0 with Everton to maintain their unbeaten starts - and with Tottenham and Arsenal making solid starts as well, it looks as though the Premier League title race could be one of the most open and fascinating for years. I go for what I felt and what I watch in the game.
Newly-promoted Wolves nearly produced the shock result of the weekend when leading 1-0 late in the game over Arsenal at the Etihad Stadium, but eventually had to settle for a 1-1 draw, a scoreline matched at [10.0].
Guardiola was in relaxed mood in the post-match press conference but appeared het up when going over to Raheem Sterling at the final whistle - a player who appeared to irk Juan Mata by doing stepovers at the end.
Ivan Cavaleiro's 13th-minute strike put Wolves ahead after capitalizing on a mistake by Granit Xhaka.