Greenwood, 17, became the youngest United player to score in Europe with the winner in a 1-0 victory against FC Astana in the Europa League on Thursday night and Solskjaer believes the club's decision to let Lukaku move to Inter Milan without signing a replacement has been justified.
"For me it was the right decision for the club," Solskjaer told a news conference. "He is going to be important for us this season. He's not played a lot so far, but he'll get minutes."
Greenwood started in a youthful team that also included Angel Gomes, Tahith Chong and Axel Tuanzebe. United are keen to secure Greenwood's long-term future with a new contract and Solskjaer revealed the club are already in negotiations.
"We're always in talks with the boys, how we see the future and Mason is one we want to keep with us," said the Norwegian.
"He is learning every single day in training, training with better players and the more match time he gets the better tempo and today was a good introduction for him."
Despite watching his side kick off their Europa League campaign with a win to see them top of their group, Solskjaer insisted afterwards there was still room for improvement.
United managed 20 shots but were reliant on Greenwood's solitary goal 17 minutes from time to take home the three points.
"When you don't score in the first half from four or five massive chances you wonder if it's one of those nights," said Solskjaer.
"I didn't feel confident we'd win the game until the ref blew his whistle. We didn't play it out well and these boys need to learn that."
Nemanja Matic, who captained United on a night when Ashley Young and David De Gea were on the bench, added: "It was a hard game. First half we tried to open the game and to score a fast goal but they had a solid defence.
"It's good for the [young players] to have the opportunity to play these games. They have to use that, to work hard to get more chances."