The Gunners were edged out 3-2 in a thrilling Premier League clash at Old Trafford, having led early on.
The result cost them the chance to move up to fourth in the table but was only their second loss in 11 games.
Midfielder Partey felt there was enough in the performance to show Arsenal are still moving in the right direction.
The Ghana international told the club’s website, www.arsenal.com: “The team is improving, each and everyone is doing our best.
“I think we’re improving each day and it’s going to be good. If we want to be at the top it’s normal that we have to fight, we have to be under control and try to win the games.
“I think the team came out to win, we did everything we could, we played well, we created a lot of chances and I think that we were unlucky.”
Partey admitted he himself was still striving to find his best after a spell out injured last month.
The 28-year-old said: “For me, I have to keep on doing my best, keep trying, keep improving, try to come back to my best, because the team needs me.”
Arsenal struck in the 13th minute with a bizarre goal from Emile Smith Rowe. The youngster drove into an unguarded net after United goalkeeper David De Gea collided with team-mate Fred.
United equalised before the break through Bruno Fernandes and then went ahead in the 52nd minute with Cristiano Ronaldo’s first goal of the night.
Martin Odegaard brought Arsenal back level but then conceded the penalty which allowed Ronaldo to fire the winner.
Partey said: “They scored two goals and then a penalty. The team tried to improve, go forward and look for a goal, for the equaliser, but in the end it’s football.
“We have to forget about this game, we have to think of our next game. We have to do better and also to win.”
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