United looked poised to move into second spot in the Premier League after Bruno Fernandes fired in the opener late in the first half, but Michael Olise's last-gasp free-kick denied the visitors.
Casemiro's 80th-minute booking for a challenge on Wilfried Zaha means the Brazilian will miss the trip to leaders Arsenal on Sunday for what could be a key contest for both sides' title hopes.
"This game was important. Every game is important," insisted Ten Hag.
"Every game in the Premier League is a top game. Casemiro is obviously a really important player for us, and he is one of the reasons that we are in the position that we are now. That's Casemiro.
"But last time we beat Arsenal without Casemiro, so we have a squad, so we have to fill that gap and make a proper plan and the squad have to fill it and make sure that there is a team. We already showed how to beat Arsenal."
Casemiro came on as a late substitute in United's 3-1 victory over the Gunners in September, with Marcus Rashford's brace and an Antony strike making the difference at Old Trafford.
Palace's defence, including a first start for Chris Richards in place of the injured Joachim Andersen, did well to quiet Rashford this time around, and United looked in control until Olise's stunner on the stroke of full-time.
Ten Hag said: "Of course that's disappointing when one unlucky moment that you will concede a goal like this and then there's no time anymore to go for the win."
The result left the Gunners eight points clear of both second-placed Manchester City and United.
Palace boss Patrick Vieira was pleased to pick up the point and insisted he was focusing on the Eagles' next meeting in their tough run against top sides rather than his former club's title chase.
"I have enough on my plate thinking about Newcastle," the ex-Arsenal midfielder said.
"(Arsenal and United) will be a good game of football. I think two teams who (hope) to play Champions League football or winning the title.
"I think both teams can win the league because of the quality of players that they have. So I'll be like you, watching the game."
Palace later confirmed a second-half pitch invader, who forced play to be temporarily halted and took a selfie with Casemiro, was arrested.
"A single individual entered the field of play before being led away by security and was later arrested," a club statement read.