Rodriguez netted the victor in the 72nd minute.
Jose Mourinho's charges had the rhythm and tempo on their side after half-an-hour and looked increasingly unsafe whenever they were on attack.
Mourinho had only revealed what he said to Pogba after the derby in an interview on Saturday night and it seems the 25-year-old has already fallen short of expectations. "We played against a really formidable team today, asked a lot of questions, but everyone worked hard and did their jobs". Are they going to go back to things that they did many, many times in the season - playing with three centre-backs, with five in the back.
"Do I expect him to score goals every match? No".
Jose Mourinho has highlighted exactly how his Manchester United side must improve in order to win the Premier League title next season. "I know how to win, I believe in myself but I don't play", added the former Chelsea and Real Madrid manager.
"I'm proud for players and staff and way they have acquitted themselves today".More news: United Nations rejects Russian attempt to condemn USA 'aggression' on Syria
While that can be helpful at times it's actually detrimental more often than not for various reasons such as how it affects the team's shape or what it means for Antonio Valencia.
Manchester United: David de Gea 6 (out of 10), Antonio Valencia 6, Chris Smalling 6, Victor Lindelof 6, Ashley Young 6, Paul Pogba 6, Ander Herrera 6, Nemanja Matic 5, Juan Mata 6, Alexis Sanchez 5, Romelu Lukaku 5.
Mourinho understands what is expected at the club and is confident that he has the ability to bring success in the future.
"Everyone is flawless, apart from Romero", said Mourinho in his press conference ahead of the game. Eight titles are eight titles and three Premier Leagues are three Premier Leagues.
'I am always a great believer that the truth always comes out and it has, ' the forward told BBC WM.
It is City's third title in seven seasons and a first under the Spaniard in his second campaign in charge. But I expect you to be consistent in a certain level.