The striker completed a £72million transfer to Inter Milan on Thursday after two seasons at Old Trafford.
The 26-year-old had been wanting a move away from United all summer and it ended with him training at Anderlecht as the final details of the deal were completed.
“It was time now for Rom to go because I think we got a good deal, he’s happy, so I think both parties ended that deal as it should be,” Solskjaer said.
“Rom was injured for a while this pre-season, he didn’t participate, so I just hope for him that he’ll get a good start at Inter Milan.”
Solskjaer is confident United‘s attack will do well despite losing the option of a regular goalscorer.
“Towards the end of last season, we didn’t score a lot of goals, did we?” he said.
“And you do have players that you think will have an impact and Mason Greenwood’s pathway would have been a lot more difficult, of course if we had another forward there.
“For me, I believe Mason is going to be playing and involved a lot and when he is, he’ll score goals.”
LIVE on talkSPORT
Check out all the live commentaries coming up across the talkSPORT network this week
- West Ham vs Manchester City (Saturday, 12:30pm) – talkSPORT
- Leeds vs Nottingham Forest (Saturday, 12:30pm) – talkSPORT 2
- Crystal Palace vs Everton (Saturday, 3pm) – talkSPORT 2
- Tottenham vs Aston Villa (Saturday, 5:30pm) – talkSPORT
While Lukaku followed Ander Herrera and Antonio Valencia in making summer exits, only Harry Maguire, Aaron Wan-Bissaka and Daniel James arrived.
The Red Devils were thought to be trying to strengthen other areas but could not get deals over the line before the window closed.
“Do you know, I think when the transfer window closes it’s that great feeling of relief,” the Norwegian said ahead of Sunday’s match against Chelsea.
“Now it’s done, now we know we’re looking forward with and I’m delighted with the three we’ve signed.
Click Here: watford football shirts