Erik ten Hag criticised Manchester United's lack of killer instinct after Michael Olise's superb stoppage-time free-kick rescued a 1-1 draw for Crystal Palace on Wednesday.
Ten Hag's side led through Bruno Fernandes' first half strike at Selhurst Park as they looked to record their longest winning streak in 14 years.
But Olise halted United's run at nine successive victories in all competitions when he smashed a breathtaking set-piece past David de Gea in the final seconds.
It was a major blow for United, who had hoped to climb to second place in the Premier League and put pressure on leaders Arsenal ahead of their visit to the Emirates Stadium on Sunday.
"When you're winning with two minutes to go and Palace don't create anything except one from a corner and one from the free-kick, you don't expect to drop points," Ten Hag said.
"We have to invest more to get that second goal and then not be in that situation that a lucky moment costs you.
"In the second half we had a lot of space to kill them and go for the second goal.
"I never saw we really went for the second goal. It's difficult to say why. I have to criticise my team. Go for the second."
Having beaten City 2-1 in the Manchester derby on Saturday, United left freezing south London disappointed not to make it 10 in a row.
Instead, United moved up to third, level on points with champions Manchester City and eight adrift of Mikel Arteta's table-toppers.
City would go three points clear of United if they beat Tottenham on Thursday.
United, who haven't won the title since 2013, can still put a little pressure on Arsenal if they beat the Gunners in north London.
"We have to take the lesson. You can't change it (the end of the winning run). We're looking forward," Ten Hag said.
"Look to Arsenal and make a proper plan. The players have to make sure they're ready."
Palace beat United on the final day of last season at the dismal culmination of Ralf Rangnick's lacklustre reign as interim boss.
United have been revitalised by Ten Hag in the intervening eight months and the contrast between the two eras was immediately evident.
Ten Hag's team went close to an early opener when Luke Shaw fizzed a half-volley just wide of the far post from Aaron Wan-Bissaka's pass.
Wout Weghorst was making his United debut following his arrival on loan from Burnley after his spell at Besiktas was cut short.
The Netherlands striker's only sight of goal in his 70-minute appearance was a header onto the roof of the net from Shaw's cross.
- United frustrated -
After being penned back, Palace threatened when Odsonne Edouard's 25-yard blast was brilliantly tipped onto the bar by David de Gea.
United were unfazed and took the lead in clinical fashion after 44 minutes.
Fernandes scored United's controversial equaliser in the Manchester derby on Saturday, with Marcus Rashford clearly offside before the Portugal midfielder netted.
There were no doubts about this one as Christian Eriksen swept into the Palace area and cut his pass back to the unmarked Fernandes, who took a touch before shooting powerfully past Vicente Guaita from 12 yards.
United maintained control for much of the second half, aided by an influential display from Brazil midfielder Casemiro, who was so unruffled he even posed for a selfie with a pitch-invading fan.
Stewards were slow to react to the supporter, who stood next to Casemiro for several seconds and was almost off the pitch again before he was finally intercepted by security.
But, to Ten Hag's chagrin, United faded in the closing stages.
Marc Guehi's header almost brought an equaliser as De Gea palmed it away.
And Palace snatched their leveller at the death when Olise bent a sublime free-kick over the wall and in off the bar from 30 yards.