The Manchester United manager praised the 22-year-old but criticised his side's defending after goals from Robin van Persie and Nemanja Vidic secured a 2-1 victory at Old Trafford
The 22-year-old was handed a start ahead of fellow forward Chicharito for the Premier League clash, and despite not getting on the scoresheet, proved a thorn in the side for the opposition defence throughout.
"Danny was fantastic," Sir Alex told MUTV. "I thought he gave them a real hard day of it, the two centre-backs.
"He and Robin [van Persie], particularly in the first half, gave them a very difficult time.
"The reason Danny played was because we wanted someone who would drop on top of their centre-midfield player. He did that well and put in a great shift.
"He ran his legs off today and deserved the man-of-the-match award really."
Welbeck's strike partner Van Persie also came in for praise from his manager, with the ex-Arsenal man opening the scoring before sending in the free kick for Nemanja Vidic to score what would prove to be the winning goal.
"It was great build-up, terrific football, and a great finish by Robin but we should have been three or four up," added the boss. "I thought we should have had a penalty when Shinji was brought down.
"All in all, it was an engrossing game as we expected in a Manchester United-Liverpool match. It's full of emotion, intensity and it's great to win them.
"I think winning is important - it doesn't matter what league position we are in. I've said many times it's a fantastic challenge between the two most successful teams in the country. I think those three points today are very, very important ones."
The Red Devils defence and goalkeeper David de Gea were subject to criticism, however, with Daniel Sturridge allowed to hand Liverpool a lifeline after his second-half introduction.
"I've not seen their goal again," he admitted. "But, to me, it looked a bit soft for us. Once again, the goalie has parried one out and there's nobody following in on the rebound.
"It did lift them but some of our defending was a bit erratic and desperate even at times. But we managed to get through it. There was a period of three or four minutes where they were shoving players into the box and some interchange between players that we had to defend very well.
"We got through that and the name of the game in the big matches are the moments where you have to defend. Today was one of them."