United were beaten 1-0 by the Dutch club at De Kuip in Rotterdam in their Group A opener after Tonny Vilhena scored in the 79th minute.
Mourinho was bitterly disappointed with the result as he felt the Red Devils were controlling the game before having some misfortune late in the contest.
"Of course I'm not happy with the start," said Mourinho.
"I think in the second half the game, in my opinion, we were always in control.
"We were trying to win and they were trying not to lose. We felt like they were collapsing a bit physically, they were in trouble and it was that moment in which we lost the game.
"It was double unlucky because it was a clear offside [for Feyenoord's goal]."
United will return to England to prepare for Sunday's trip to Vicarage Road to take on Watford in the Premier League.