A 6-2 first-leg victory at Old Trafford meant United already had one foot in the Gdansk final ahead of the trip to Italy, where Roma made things uncomfortable and won an entertaining semi-final second leg 3-2.
Solskjaer said he was disappointed with the second-half display during which his team conceded three times.
But he praised Cavani - who followed his first-leg double with another two goals in Rome - as well as De Gea, whose position has this season come under increasing scrutiny with Dean Henderson's emergence.
Edinson has shown again why we want to keep him at Old Trafford.
"Football has its own language. Edinson has proven tonight, in previous games and throughout his career what a centre-forward should be doing both on and off the ball, both preparing for games and recovering from games.