It followed their 1-0 victory in Spain on 4 May.
With United struggling to secure a top four finish in the Premier League and access into next season's Champions League, winning the Europa League is a guaranteed way of reaching European club football's most prestigious tournament.
But Mourinho said it would be wrong purely to view the final in those terms.
"The final means an opportunity to win a trophy as well as the opportunity to be back in the Champions League," said the Portuguese, who won the Uefa Cup - the precursor to the Europa League - with Porto in 2003.
"It means an opportunity to end the season in the perfect way because the final is the last match of the season."
United are sixth in the Premier League with 65 points. With three games until the end of the season on 21 May, his players need to win those fixtures and hope that Liverpool, Manchester City and Arsenal fail to replicate that consistency.
Ajax - United's opponents in the Stockholm showdown - end their campaign on 14 May and will have just under two weeks to hone themselves for their first European final since their Champions League defeat against Juventus in 1996.
"Obviously now Ajax think about the final," Mourinho said after the second leg. "Their league finishes on Sunday and they will have time to prepare for the final while we have three Premier League matches to play.
"Hopefully Crystal Palace don't need the last game to maintain their Premier League status because in the last game I'm going to make a lot of changes and nobody can blame us because we have a final a few days later."
Edgy and ugly
United appeared to be cruising towards the final. They doubled their aggregate advantage in the 17th minute when first leg match winner Marcus Rashford crossed for Marouane Fellaini to head home.
However, it became edgy and ugly in the closing stages after Facundo Roncaglia levelled on the night with five minutes left. He was sent off following a shoving match with United defender Eric Bailly.
Vigo's Claudio Beauvue shot rather than crossed when he found himself six yards from goal in stoppage time and Vigo striker John Guidetti also missed the target.
Despite their elimination, Vigo coach Eduardo Berizzo hailed his players.
"You learn from defeats and eventually down the line you hope to turn those defeats into victories," said the former Argentina defender.
"I couldn't be more proud of my players. They covered every blade of grass. I'm proud of the connection they made with the fans that travelled all the way from Galicia.
"Every defeat is bitter. But when you look back on it and analyse it, I think it'll confirm what I've thought about my team all season. We've had a fantastic season. I can't blame my players in any way. We couldn't quite turn our dream into reality, but we showed great bravery out there."