Ibrahimovic, who scored 28 goals in all competitions before he was hurt in the quarter-final win over Anderlecht, celebrated with his team-mates at the Friends Arena after goals from Paul Pogba and Henrikh Mkhitaryan clinched the only European trophy missing from United's collection.
Midfielder Juan Mata added: "It was a very hard week for a lot of us and for the city of Manchester and we tried to win for all the people who have suffered". We are just football players but we have an audience so we want to work together for a normal world.
The United manager said his biggest failing revolved around his difficulties working with players who have "a different mentality to what I have" and that he has to lean on his assistants to try to coax the best out of such players. However, after Manchester United's win on Wednesday, Mourinho looked the happiest of the lot. Maybe. But we just came to do our job.
Pogba told BT Sport: "We know that things like this are very sad, all over the world: in Manchester, in London and in Paris, too".
"We just came to do our job and the boys were fantastic because they blocked (it out), they put a wall in front of their eyes and they stay isolated from everything".
United's triumph followed success in the League Cup and the Community Shield in Jose Mourinho's first season in charge at Old Trafford with Champions League football secured after United could only manage a sixth-place finish in the Premier League. "People say we've had a bad season but the prize is great and we've done it now".
The win preserved Mourinho's ideal record in major European finals, adding to his 2003 UEFA Cup victory with FC Porto, and his Champions League triumphs with the same club in 2004 and Inter Milan in 2010.More news: Oil falls as OPEC prepares to extend output cuts
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"It means everything. It means the third trophy, it means going back to the Champions League, it means winning a European trophy, it means playing European Super League in Macedonia next August". The club now has every title in world football.
"We're obviously disappointed", the Dutchman said. "We didn't. I haven't seen the Ajax that I'm used to". "We got up there and we are very proud now".
'I think it's so unfair what happened to him, ' said Mourinho. "But nobody will remember any of that, all they will remember is that they won the trophy this year, and they're in the Champions League next year".
"We didn't have many chances".
"I think there's a big difference in how the teams play - it's not about strength but how you use your bodies".
"I suppose the argument would be, if you're a United supporter getting to a cup final, it doesn't really matter how you play, as long as you end up coming home with the cup."