Martial started as the lone striker in United's 2-1 win over rivals City, but the France international was taken off at halftime after appearing to hurt his hip.
"I hoped to avoid that he was getting injured but he was complaining," Ten Hag said. "That's why he also didn't train in the week and was a question mark (for the derby).
"We decided, and he decided as well, to start. He begged to start... But I needed to re-evaluate at halftime as you saw he was not capable to go 100% and this is what you need."
Asked if Weghorst could be involved in Wednesday's game after joining United on loan from Burnley, Ten Hag said: "I have to think about that.
"Of course, I know a lot about Palace... but the total plan I don't have now. I didn't construct it until now. So from this point on we can construct the plan and prepare the team in the right way."
United are fourth in the league standings on 38 points after 18 games, behind Newcastle United on goal difference, though Eddie Howe's side have played a game more. City are second with 39 points, while Arsenal lead with 47.
Ten Hag, whose side have won their last five league games, said the team has to consistently deliver results.
"The players have to get in the right rhythm from a physical point of view but also mentally - be ready for the next game," he added.
