Greenwood fired in a powerful goal in the 45th minute as Manchester United eased to another impressive away win to enhance their bid to finish inside the Premier League’s top four and clinch a direct UEFA Champions League spot.
The Red Devils are still fifth but within two points of third spot, now occupied by Chelsea, with Leicester City in fourth one point ahead of the Red Devils in a tight race.
Greenwood, along with Bruno Fernandes and Paul Pogba, were on the scoresheet at Villa Park, but the display of the 18-year-old English forward, who has now netted nine league goals, caught the eye.
“He has to manage himself,” Solskjaer said.
“I’m doing my bit to help him, he has to turn in performances in the training sessions and in the games, play properly.
“It’s all down to him and he can go as far as he wants to. He’s an exceptional finisher and I’m surprised he didn’t score his first chance today.
“You can’t leave a player out when he’s scoring goals. That’s more or less impossible.”
United’s opening goal came with some controversy, with the referee awarded a penalty after a collision just inside the box between Fernandes and Villa defender Ezri Konsa.
Villa boss Dean Smith fumed at a “disgraceful decision” with referee Jon Moss’ original call not overturned by the video assistant referee, but Solskjaer thought differently.
“If I try and tackle you and jump over you and I land on you, I think that’s a foul,” the Norwegian said.
“The boy sticks out his leg, he (Bruno) does a fantastic Maradona pirouette and he lands on him and I think its a penalty.”
United are next in action on Monday at Old Trafford against Southampton.