Ten Hag bemoans Man United's lack of killer instinct after goalless Palace draw
Alejandro Garnacho and Bruno Fernandes hit the bar for the visitors in the first half as United dominated on a ground where they were thrashed 4-0 just four months ago.
But only a stunning double save from Andre Onana after the break denied Palace their first league win of the season.
A point leaves United down in 11th after winning just two of their opening five matches of the new Premier League campaign.
"I'm not content, we should have won," said Ten Hag. "First half we left them alive, the second half was more balanced.
"We played very good (in the first half), total control of the game, the only thing was in the box and in the box is where the game is decided. We should be more clinical there."
The humiliation of their last visit to Selhurst Park in May was the nadir of a troubled season for United.
Many wondered whether Ten Hag would even oversee another match but a shock FA Cup final victory over Manchester City handed the Dutchman a second chance.
The Red Devils this time arrived in south London on a high after scoring 10 goals in the past week to dispose of Southampton 3-0 and smash Barnsley 7-0 in the League Cup in midweek.
Marcus Rashford had ended a barren run by scoring three times in those two matches, but he was surprisingly dropped to the bench by Ten Hag.
However, the decision to keep Garnacho on the left was inspired as the Argentine tore Palace to shreds early on without applying the final touch.
Former United goalkeeper Dean Henderson kept the Eagles in the game before half-time.
Garnacho did not get enough on his curling effort to beat Henderson with his first big chance before the England stopper denied Matthijs de Ligt and Lisandro Martinez.
United knew their luck was not in when the visitors then hit the bar twice in the matter of seconds.
Garnacho sprinted onto Diogo Dalot's incisive pass to curl off the woodwork before Fernandes' follow-up effort also clipped the bar.
'Pitiful' point
Palace boss Oliver Glasner reacted with a double substitution at half-time which resulted in a far more competitive second half.
"In the first half we needed a great goalkeeper and fortunately we had one today," said Glasner.
"In that second half it was more like a Crystal Palace team and that is what we need to be competitive against a team like Manchester United."
Fernandes was inches away once more with an audacious outside-of-the-boot effort that flew wide after a neat one-two with Joshua Zirkzee.
But only a moment of magic from Onana prevented United from slipping to a third defeat in five league games this season.
The former Ajax 'keeper got down well to parry Eddie Nketiah's strike from distance before leaping off the ground to prevent Sarr tapping in the rebound.
"It's not so important (how I made the double save) because we didn't win," said Onana. "Unfortunately we didn't score. It's pitiful to go back home with the one point when you deserve to win."
Palace had another huge chance to snatch all three points when Eberechi Eze side-footed wide with the goal gaping from close range.
A draw leaves Palace down in 16th, but it is United who will be more frustrated with the missed opportunity to gain some momentum with three wins in eight days.