The Derby, which produced only two shots on target, moved Manchester City to the top of the Premier League table on goal difference, level on points with second placed Arsenal, and Manchester United in fourth, two points behind both City and Arsenal.
The best chance of the game, fell to Manchester United’s substitute, Jesse Lingard who volleyed the ball against the crossbar following a flick pass from Anthony Martial.
At the end, Manchester City boss, Pellegrini looked the more satisfied, he commended his players for their brilliant and organised defending.
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Pellegrini said: “We are back at the top of the table, I prefer to play in another way but we defended well.
“It was very tactical. Unfortunately it was not a very attractive game.”
Manchester United boss, Louis Van Gaal, also applauded his players for their focus and concentration, admitting the game was tough.
The Dutch man told news men: “I am proud of my players. They have been concentrating and focused for 90 minutes.
“We didn’t create much but City adapted their line-up to our line-up. It was tough.”
Meanwhile, Liverpool’s new coach Jurgen Klopp will have to wait for his first win, as a late Sadio Mane’s equaliser meant both Liverpool and Southampton shared the spoils in an entertaining 1-1 draw at Anfield on Sunday.
A powerful header from Substitute, Christian Benteke in the 77th minute had put the host in front.