Solskjaer was full of praise for the forward but has urged Greenwood to improve his heading ability as he looks to shape his all-round game.
"He had a fantastic season last season," Solskjaer said after the game. "To get his goal was important for him, and Marcus (Rashford), it is always nice for strikers to get that confidence and that feeling of scoring - to get that hunger again.
"He can play through the middle, I think as a young boy - not physically grown yet, sometimes it is nice to be facing forward instead of being the foil and being the battering ram.
"I scored most of my goals from just outside the posts as well, I wasn't in the middle.
"For him to be a number nine, though, he needs to learn how to head a ball. I keep telling him that and if he wants to do that he is welcome to come and practice with me."
Solskjaer conceded he did not originally plan to introduce his trio from the bench but felt Luton pushed his side hard as he looks to get his players back to match sharpness.
"It wasn't planned for them to play,' he said. 'I don't plan ahead that much, you just see wherever you have to to make changes.
"They have a decent training session tomorrow so I didn't want them to play too much.
"They did well coming on, got their runs in, got the work in. You can see we need match time, these players need match time for sharpness.
"The levels in English football are getting better, that was their cup team as well so the standards are high in the Championship. They have done well and made us work hard to go through."