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.
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.
It was a day of flashpoints of fan unruliness in English soccer with two fans arrested in high-profile incidents.
A supporter also managed to invade the Emirates Stadium pitch after Aubameyang scored, pushing United defender Chris Smalling in an attempt to join the celebrations before being stopped by stadium security.
In high winds and occasional driving rain, Liverpool fought back against Burnley, which took an early lead at Anfield in the sixth minute when Ashley Westwood's corner curled straight into the far top corner of the net.
"We had the perfect mixture of fighting the opponent, fighting the circumstances and playing football. That was really good and I liked it."
At Stamford Bridge, Chelsea winger Eden Hazard exploited a Wolves defensive lapse to strike his 13th league goal of the season in the second minute of stoppage time to cancel out Raul Jimenez's opener.
"When you have to play only 10 matches, every match you're not able to win is a missed opportunity," Chelsea manager Maurizio Sarri said.
"In the last six matches, we won four matches and drew the other two. So there is a little consistency in this moment. We have one match in hand, so we have to be confident."
Wolves are seventh in the standings but 13 points behind Chelsea.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)