"We outperformed them, so it was a positive outcome for Manchester United," Mourinho stated in an interview with TNT Sports.
A point leaves United languishing in 21st of the 36-team table and with their chances of securing a top-eight finish to progress directly to the last 16 fading.
Fenerbahce are in 14th on five points, with a top-24 finish enough to qualify for the playoff stage.
Mourinho also came into the game under pressure early in his reign with Fenerbahce trailing rivals Galatasaray by eight points at the top of the Turkish Super Lig.
"If we play like this in the Turkish league, we destroy every team," added Mourinho, who was shown a red card for his protests after appeals for a penalty were waived away in the second half.
"He (the referee) told me something incredible. He could see the action in the box and my behaviour on the touchline.
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"I congratulate him because it is incredible his peripheral vision. During the game, 100 miles per hour, he had one eye on the penalty situation and one eye on the bench and my behaviour. That is why he is one of the best referees in the world."
United were without 10 players, including captain Bruno Fernandes, due to suspension or injury.
In Fernandes' absence, defender Noussair Mazraoui started in an unfamiliar attacking midfield role and had a part to play in an impressive opening goal.
Manuel Ugarte dispossessed former United midfielder Fred to launch a counter-attack that involved Alejandro Garnacho and Mazraoui before Joshua Zirkzee teed up Eriksen to blast home from the edge of the area.
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However, for the third time in three Europa League matches, Ten Hag's men failed to build on taking the lead and have now gone a full calendar year without winning a European game.
"We have to win and we get again in the position to win, but we have to be killing (the opponent off) more," said Ten Hag. "We let the opponent get away with the point."
- Onana double-save -
Ugarte has struggled to establish himself since arriving in a £50 million ($65 million) deal from Paris Saint-Germain in August.
But the Uruguayan showed the defensive awareness that attracted United's interest with a brilliant goal-saving challenge to deny Dusan Tadic a tap-in.
United also needed an excellent double save from Andre Onana to parry two En-Nesyri headers to protect their lead at half-time.
It was wiped out within four minutes of the restart as more sloppy defending allowed En-Nesyri to head in Allan Saint-Maximin's inviting cross.
Fenerbahce were furious moments later when penalty appeals for a foul on Bright Osayi-Samuel were waived away.
Mourinho took his protestations too far as he was dismissed by experienced French referee Clement Turpin.
There remains plenty of time for United to dig themselves out of trouble with five more favourable looking Europa League fixtures to come against PAOK, Bodo Glimt, Viktoria Plzen, Rangers and FCSB.
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However, whether Ten Hag will still be in charge for all of those fixtures remains a major doubt after winning just four of United's opening 12 games of the season.
(Except for the headline, this story has not been edited by staff and is published from a syndicated feed.)