After 12 unbeaten matches across three months since Jose Mourinho's firing, United finally lost in the league under the interim manager.
Granit Xhaka's swerving – potentially wind-assisted – strike flew past goalkeeper David De Gea in the first half. Pierre-Emerick Aubameyang netted a second-half penalty to give Arsenal a 2-0 victory after Alexandre Lacazette was bundled over in the penalty area by Fred.
"You have to be disappointed with the result," said Solskjaer, who had 10 wins and two draws in the league. "But the performance, as you say, was a good one."
Arsenal and United were once slugging it out for the title in the era of Alex Ferguson and Arsene Wenger. Now they are in a chase for fourth place. Arsenal displaced United in the final Champions League qualification spot, sitting two points in front.
The title challenge is down to two teams, and Liverpool trimmed Manchester City's lead back to a point after coming from behind to beat Burnley 4-2.
Chelsea, which won the title two years ago, remains down in sixth place after behind held 1-1 by Wolverhampton but is only one point behind United.
"I don't think nerves go into it yet. Spurs lose (at Southampton on Saturday), we lose, Chelsea draw," Solskjaer said. "It is going to be down to the wire. Down to the last few games. Definitely. We've given ourselves a great chance to be in that fight."
United has displayed its perseverance already in the last week, scoring a stoppage-time goal at Paris Saint-Germain to advance to the Champions League quarterfinals.
"It was maybe backlash from Wednesday night," Solskjaer said of the loss at Arsenal.