The striker led the line in the absence of Edinson Cavani and impressed throughout.
Despite not scoring he was instrumental in everything good for United as they ended City’s unbeaten run.
In the first minute of the game, Martial won a penalty for his side which Bruno Fernandes converted.
Solskjaer was impressed with the striker and also singled out Dean Henderson for his performance in goal.
He said on Sky Sports: “When you come away with a 2-0 win and another clean sheet and a performance like this then you are delighted.
Meanwhile, Man City boss Pep Guardiola congratulated United for the way they won at the Etihad.
He explained: “It was a fantastic game. United make incredibly high pressing and they are so fast on the counter.
“We played good. Unfortunately we couldn’t be clinical up front so we congratulate United.
“We will be the news because we lost. But the news is 21 victories in a row. There are still 30 points to play and we have to start to win again.
“That’s football. Sometimes it happens. We played much better than the game against West Ham which we won.
“It’s always the same. We win a game and then move onto the next one. It’s the same here. We lose this so we go to the next one. It’s a lesson. Even at 0-2 we played really well.”
United return to action on Thursday against AC Milan in the Europa League.
After that Solskjaer’s side face West Ham in the Premier League as they look to secure second place and push City all the way.