The Norwegian has put the club on an upward trajectory since he replaced the sacked Jose Mourinho in December, with 10 Premier League victories and two draws ahead of the Arsenal fixture, Eurosport reported.
However, that unbeaten run came to an end on Sunday, with a 2-0 loss at The Emirates that left United two points adrift of Arsenal in fifth.
Solskjaer said, "The performance was good but the result was disappointing."
"We are disappointed with the result but looking at the performance, you cannot say it was a game we deserved to lose. We created five big chances, hit the woodwork twice.
"When you see the boys work as hard as they do, the attitude they show in training – today we were lethargic in the first 10-15 minutes, did not have the zip and we did not take the chances. Hopefully we will be ready for Wolves in the FA Cup next week.
“It has been fantastic so far but today is the lowest we have been because we lost and missed the chance to put pressure on Spurs."
"We have won games we have not deserved to win, and today we lost a game we did not deserve to lose."
Solskjaer’s opposite number, Unai Emery, praised his goalkeeper Bernd Leno for keeping the visitor at bay.
"I am very proud of our players,” he told BBC Sport.
“They gave all they could against the best team at this moment.
"We were playing very competitive for 90 minutes and I think we deserved this victory. We can be happy today.
"We knew Manchester United could use different tactics but we wanted to impose our gameplan and I think we did that.
"Our goalkeeper is very important and sometimes the goalkeeper can save us, and today I'm very proud of his work."