United was playing in the group stage of European club football's second tier competition for the first time in its history, but it was an underwhelming start as the Dutch hosts won 1-0 thanks to Tony Vilhena's late goal.
Feyenoord coach Giovanni van Bronckhorst commended the spirit and determination shown by his team -- qualities Mourinho fears three-time European champions United will face in every game in Group A, where Turkish side Fenerbahce and Ukraine's Zorya Luhansk drew 1-1.
"We know that when Manchester United goes in the Europa League, we are the team that everyone wants to play against, that everybody wants to fight (against) until their limits, which they did," Mourinho told British television.
"Feyenoord defended with everything -- a great crowd, a great spirit. Some of our players were playing their first minutes of the season. Obviously some played better than others but I cannot judge them just for a game."
United may never have won the Europa League but an indication of its priorities came from the fact that only David de Gea, Paul Pogba and Eric Bailly were retained from the side that lost Saturday's Manchester derby.
Wayne Rooney, Antonia Valencia and Luke Shaw may have been resting in England ahead of Sunday's Premier League at Watford but there was still plenty of experience with Juan Mata, Ander Herrera and Chris Smalling all starting.
Since winning the Europa League's forerunner, the UEFA Cup, with Porto in 2003, Mourinho had not overseen a match in the competition, concentrating -- and winning -- the Champions League instead, with the Portuguese side in 2004 and Italy's Inter Milan in 2010.
United are no strangers to the Europa League though, having dropped into the knockout rounds under Louis van Gaal
and Alex Ferguson, but this was the first time the club had entered at the group stage -- after only finishing fifth in last season's Premier League.
Should they rebound and win the competition, they would become only the fifth side -- after Juventus, Ajax Amsterdam, Bayern Munich and Chelsea -- to win the European Cup/Champions League, the Uefa Cup/Europa League and the defunct Cup Winners' Cup.
Elsewhere, Ajax -- who have been crowned European champions four times -- played Panathinaikos in a repeat of the 1971 European Cup final, which the Dutch side won.
They were victors again in Greece on Thursday, winning 2-1 under new coach Peter Bosz.
Bosz was appointed after Frank de Boer left Ajax in August in charge but the former Dutch international is finding life difficult at new club Inter Milan.
His poor start to the season intensified worse when Inter lost their maiden Europa League match 2-0 at home to Israel's Hapoel Be'er Sheva in Group K.
Arguably the game of the night involved another Israeli outfit as Maccabi Tel Aviv led Zenit St Petersburg 3-0 with 13 minutes left in Group D only to lose 4-3 as the Russians scored a 91st-minute winner.