The hosts sealed a 1-0 victory through Ashley Young's 65th minute strike, which needed a massive deflection off Lewis Dunk to take it into the top right corner.
Having fought tooth and nail throughout the game and matching, if not bettering United performance wise, Mourinho highlighted some of the qualities that the Seagulls showed.
"It was a battle because Brighton were very good. I think they were good from minute one to the last minute.
"The had a good approach, defensively they were very well organised.
They usually play with [Pascal] Gross as a second striker but today they played with a line of five across the midfield.
"I keep saying defending well is very important, and they defended very well. They were quite dangerous on the counterattack because their wingers are very quick."
The first half saw Albion take the game to an under-par Red Devils side, showing more attacking intent than they had done against top six sides previously this season.
United's frustrations with how the game was going saw them pick up the pace after half time, with Albion pressing continuously for an equaliser in the final 25 minutes of the game.
Whilst he praised his own team for holding onto their lead, the former Chelsea and Real Madrid manager again showered the Seagulls with plaudits.
"The good thing for me was the intensity got higher in the second half in search of a goal. After the goal we couldn't kill the game and in the last 15 minutes I saw a team with everybody trying to play for the clean sheet and giving everything.
"I'm happy with the attitude but I have to praise a team and a manager that a few months ago were playing in the Championship.
Today they came to Old Trafford and they were the team that, up until now, have given us the most problems this seasn."
There was some controversy surrounding the build-up to the home side's goal at Old Trafford.
Albion remonstrated with the officials over a corner kick awarded against Solly March, in the belief that the final touch came off United striker Romelu Lukaku.
The clearance from the following set piece fell to Ashley Young for the winning strike.
Having yet to see a replay of the incident after the match, United's boss wasn't in a position to say for sure if it was the correct decision.
"The corner was the other side of the pitch. I just think Lukaku was phenomenal in fighting for that ball and the linesman is two metres.
"I am over 80 metres away, so I have no idea."
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