In the first half, Alejandro Garnacho and Bruno Fernandes both came close to scoring for the visitors with shots that hit the crossbar. Despite their strong performance, Manchester United were reminded of their 4-0 defeat on this ground 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.