A 79th-minute strike from midfielder Tonny Vilhena punished a lacklustre display from a United side that was much-changed but still contained almost £300m worth of signings.
Consecutive defeats, following last weekend’s 2-1 derby loss to Manchester City, represent an embarrassing blow so early in Mourinho’s first season, yet he insisted his team had been hard done by.
“In the second half we were always in control, we were trying to win the game and they were trying not to lose,” he said.
“In that moment we were pushing and they capitalised because it is exactly at that moment where we lose the game. We were double unlucky because it’s a clear offside.
“They defend with everything, with a great crowd, with great spirit. We know that. We know that when Man United goes to the Europa League we are going to be the team that everybody wants to play against, that everybody wants to fight to their limits, which they did and they had the luck on their side to score a goal in the last part of the game.”
Mourinho made little attempt to hide his disdain for the Europa League ahead of this first Group A fixture and made eight changes from the City game, yet £89m world record signing Paul Pogba started.
Pogba again struggled to influence the game, despite being afforded greater licence to get forward in Wayne Rooney’s absence, and lone striker Marcus Rashford was left isolated.
Mourinho threw on top scorer Zlatan Ibrahimovic as part of a second-half triple substitution but instead it was Feyenoord, coached by former Arsenal midfielder Giovanni van Bronckhorst, who struck.
Striker Nicolai Jorgensen appeared to stray offside when running onto a pass down the right but the assistant’s flag stayed down and he pulled back for Vilhena to plant a low shot past David de Gea.
Southampton made the perfect start to Group K and claimed their first win under new coach Claude Puel as they beat Sparta Prague 3-0 at St Mary’s Stadium.
Striker Charlie Austin put them in front with an early penalty and headed a second on 27 minutes. Shane Long set up Jay Rodriguez to slot the third in stoppage time.