The 46-year-old Norwegian has enjoyed a remarkable run since being named as interim manager on December 19 following the dismissal of Jose Mourinho, winning 14 games, drawing two and losing just twice.
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.
"We are disappointed with the result but looking at the performance, you can not say it was a game we deserved to lose".
"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".More news: The Prodigy Frontman Keith Flint's Cause of Death Revealed
Pochettino's men do have the slight relief of a three-week break now to regroup, but their next league game is a daunting one away to Liverpool and they also travel to title-chasing Manchester City next month.
Solskjaer is expected to be given the United job on a permanent basis thanks to his incredible record since taking caretaker charge, particularly after eliminating Paris Saint-Germain to reach the Champions League quarter-finals.
As for Chelsea, they face a trip to Anfield in addition to that game at United and, like Arsenal, must juggle league games with Europa League commitments.
"I was stood right behind the ball and we don't put enough pressure on Xhaka, who must be Brazilian by the way because he struck the ball and it swerves and moves".
Solskjaer said: "The performance was good but the result was disappointing".More news: Chance the Rapper ties the knot in star-studded wedding
Romelu Lukaku and Fred both hit the woodwork for the visitors, while goalkeeper Bernd Leno made saves to deny Lukaku, Paul Pogba and Marcus Rashford.
Manchester United will reportedly confirm Ole Gunnar Solskjaer as their new permanent manager during the upcoming global break.
Emery told BBC Sport: "I am very proud of our players".
"Being competitive like today for 90 minutes can give us a stronger mentality".
"We don't play against the other top six teams so I think we can beat the others", the goalkeeper added.More news: Brexit vote still a go for Tuesday but pessimism abounds