Lewis Dunk's unfortunate deflection from an Ashley Young shot in the 66th minute proved the difference at Old Trafford on Saturday.
The lone goal came following a Marcus Rashford corner, which Chris Hughton argued should have been a goal-kick due to an apparent touch from Romelu Lukaku.
But the Red Devils boss was not prepared to weigh into the discussion other than to praise his Belgian striker's determination.
"The corner is on the other side of the pitch. The linesman was two metres away, I am maybe 80 metres away, I have no idea," Mourinho said at his post-match press conference.
"I just think Lukaku was phenomenal in his effort to fight for the ball."
39 – @ManUtd have gone 39 games in all competitions without defeat at Old Trafford (W28 D11), last losing to Man City in Sept 2016 – 441 days ago. Theatre.— OptaJoe (@OptaJoe) November 25, 2017
Mourinho admitted his team "did not play well", but took heart from the way they negotiated the tense closing stages.
"I saw everybody playing for the clean sheet and giving everything," he said.
"People like Lukaku playing wide on the left and chasing defenders, the midfield players closing the space in the middle. So I am happy with the attitude."