Liverpool had won their previous five games in all competitions but they were stifled by Jose Mourinho's side during the draw at Anfield on Monday. Two shots on target - with 65 percent of possession.
Another former United player, Ray Wilkins, said the pressure of expectation on Mourinho is relentless.
United became the first side to take a point from Anfield this season when they stifled Liverpool in a dour stalemate on Monday.
But United restricted them to few chances, with visiting goalkeeper David de Gea largely untroubled apart from a pair of eye-catching second-half saves to deny Emre Can and Philippe Coutinho.
"I think you are very fair with Liverpool because Liverpool had a fantastic defensive performance", the United manager said on Wednesday afternoon.
"We knew their transition when they lose the ball is really strong and high, so we adapted to the situation".
"I think we've been unlucky with the worldwide break because I felt momentum when we played before the global break", he said on LFC TV.
United had just 35% possession in the game, the lowest total in a Premier League match for the Red Devils since Opta began recording this data in 2003-04.
"When we got the ball I was expecting the team to be more risky, (although) we had two good chances. but Liverpool did too. At that moment I thought it would be hard to win now, so let's not lose it".
The England global was replaced by captain Wayne Rooney in the 77th minute against the Merseyside outfit, and United's Portuguese boss said that that was due to the teenager suffering from cramp. When they want to chase us, we have to use counter-movements.
"Second half we managed better to get through but United defended well with De Gea making top saves".
That was the game that we played - we don't control the game by having the ball all the time. That is not the way we want to play, but I accept it.
Manchester United frontman Zlatan Ibrahimovic has admitted that he should have done better with his glorious headed chance against Liverpool.
"We started OK and immediately with their defending we weren't fearless anymore".