Cavani scored twice in each game while De Gea produced some fine saves as United advanced 8-5 on aggregate.
Ole Gunnar Solskjaer heaped praise on Edinson Cavani and David De Gea after Manchester United kicked off a run of four matches in eight days by reaching the Europa League final.
Having beaten Roma 6-2 in last week's semi-final first leg at Old Trafford, the Red Devils sealed their shot at glory against Unai Emery's Villarreal on May 26 despite losing the return leg 3-2 on Thursday.
Cavani scored twice in each game while De Gea produced some fine saves as United advanced 8-5 on aggregate.
"I was disappointed with of course conceding so many shots and so many goals. It was always going to be an open game because they had to score goals and that was going to make it a chance for us to create chances," said Solksjaer.
"I think both teams could have scored five more, so it could have been 6-6, 7-6, it could have been a different scoreline. But for me now the main thing is we're in a final, we know we have to play better than this but we're here because we've had a centre forward who has scored four goals during the tie, during the two legs. Edinson's shown again why we want to keep him at Old Trafford," he said.
Cavani, who is out of contract this summer, grabbed the goals but De Gea shone brightest. The long-serving number one flourished at the Stadio Olimpico, staking his claim for a starting role in the final having been displaced by Dean Henderson in the Premier League.
"David was vital, he was man of the match for me, standout performer. The final is still three weeks away, so we've got many games but David's put in a very good application in by his performance," said Solksjaer.
"Proof is always on the pitch. You've got to perform and you keep your place in team when you play well," he said.
The Europa League final offers United a chance to secure their first silverware since winning the competition in 2017, but they have a lot to deal with before then.
The postponed clash against Liverpool has been rearranged for next Thursday, leaving the Red Devils facing four matches in a mere eight days.
After this match in Rome, Solskjaer leads his side to Aston Villa on Sunday before hosting third-placed Leicester on Tuesday and then Jurgen Klopp's men.
"It's unheard of," the Norwegian told BT Sport. "It's made by people who have never played football at this level. It's physically impossible for the players. We have not been dealt a good hand."
"We are going to need everyone for these four games. It's a short turnaround but we have to be ready," he said.
