But the Portugal midfielder answered with a stoppage time goal to earn United a narrow 1-0 win at Craven Cottage on Saturday.
"From the moment I made him captain he did this [win games]," Ten Hag told a post-match news conference.
"Always when he is playing, he is giving energy and setting the example. And you see the way he is pressing, the way he is counter pressing. The way he makes recovery runs. He is absolutely the example and he is taking responsibility all the time. On and off the pitch.
"He takes responsibility by scoring important goals but also in how he is always wanting the ball and always wanting to create. I'm happy with my captain."
The Dutchman branded Rashford's decision to attend a party after the defeat to City as "unacceptable" on Friday but insisted the 26-year-old would have started against Fulham had he not failed a late fitness test.
"He had some complaints after the training," said Ten Hag. "He travelled with us but today the complaints were that much that he couldn't start. It was a risk to start him because we might lose him over more weeks.
"So we didn't want to go with this risk because we have many more important games after today."