Rashford's loss of form has been a major factor in United's disastrous start to the season.
The England international scored 30 goals for his club last season, but has just one in 14 appearances so far this campaign.
United have lost eight of their opening 15 games in all competitions - their worst start to any season since 1962/63.
Ten Hag is under mounting pressure as City's comfortable victory at Old Trafford was followed by Newcastle's 3-0 win to dump United out of the League Cup on Wednesday.
Rashford started that match on the bench.
Ten Hag said that decision was due to rotation rather than disciplinary action.
However, he refused to confirm or deny whether the 26-year-old had been fined.
"Yes, I am aware of it," manager Ten Hag said of Rashford's post-derby night out.
"I spoke with him about it. It's unacceptable, I told him, he apologised and that's it. For the rest it's an internal matter."
Ten Hag, though, insisted Rashford, who came through the United academy, remains as committed as ever.
"He's very motivated to put things right. I know which effort he is putting in. He's totally with us," added the former Ajax boss.
"So, he makes a mistake, but that doesn't say he's not fitting in. I see him every day in training, what he's doing.
"Also, off the pitch, what he is doing, how he lives, and I'm sure he is doing everything right to help the team to perform and to let us win."
Ten Hag also backed Rashford to refind his scoring touch to get United back on track.
The Red Devils face a tricky Premier League trip to Fulham on Saturday before a vital Champions League clash at FC Copenhagen in midweek.
"He has to be as close as possible to the opponents' goal, because there are his qualities," said Ten Hag of rediscovering Rashford's best form.
"There he is so important for us and he will contribute so much to our success.
"We have to get him there as a team and he, as an individual, also he has to make his movements to arrive in the right moments, so his timing is right and I'm sure he will be back."
