Second-half goals in the space of three minutes from Granit Xhaka and United old boy Danny Welbeck condemned United to a first defeat in 26 Premier League games.
The result left United in fifth spot, four points behind local rivals Manchester City, with just three games to play and Mourinho has written off his side’s prospects of qualifying for the Champions League via the domestic route.
Instead, Mourinho is focusing on booking a spot in next season’s Champions League via the Europa League, with United holding a 1-0 lead over Celta Vigo ahead of Thursday’s semi-final second leg at Old Trafford.
"Yeah, all on the Europa League,” Mourinho, who rested several key players, told Sky Sports after he suffered his first Premier League defeat against Arsene Wenger.
“Like we did today, we tried to play for a result.
“You can tell me we didn't play with the best players, or the first choice at the moment, but you can't say we didn't try to win the game. And that's what we're going to try and do in the next three Premier League matches."
Despite the defeat, Mourinho was eager to praise his team's performance and could find no fault with the likes of Phil Jones, Chris Smalling and Juan Mata, who were all making their first starts following extended spells on the sidelines.
"I liked very, very much individual performances and I liked [them] collectively," Mourinho said.
"We lost because we didn't score and we had great chances to. They had the luck of [the first] goal.
"Apart from that, I cannot ask more from players who do not play one minute of football in the past seven weeks like Smalling and Mata. They were amazing the way they performed.
"The kid [Axel Tuanzebe], the same. I think he did an amazing job and I think Alexis [Sanchez] knows his name because the kid really played very well.
"It was difficult for me to manage the game because the players that I wanted to replace are the players that, in principle, start the game on Thursday.
"So, difficult to manage it but I think, in principle, the team was good, was organised, played to win and defended well.
"Arsenal were not better than us in my opinion but congratulations."