Rashford was pictured partying in Belfast last week in the days leading up to their FA Cup clash against Newport County.
Ten Hag said the England international missed training due to illness but it was reported that he drank for 12 hours and passed out at 3am.
Rashford is believed to have been fined £650,000, the equivalent to two week's wages, and United said he has 'taken responsibility.'
His boss then confirmed on Wednesday that it's 'case closed', with the 26-year-old back in training ahead of their trip to Wolves.
Following the night out, Ten Hag has expressed his belief that it's up to players to deliver high standards at the club.
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"First of all, the players at this level have to manage themselves. That is what you can demand from the player," Ten Hag said.
"A player has to know what is good and what is no good. When you want to play top football, it demands a certain way of life. Always."
He added: "We are talking about top football players. I don't have to educate them anymore. When you are playing for Man United, they should know."
Ten Hag is also aware of how behind the scenes factors can affect a player's behaviour but still demands them to take responsibility.
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"Of course, that is part of the job to support your players. But also we have people in this club who are helping the players on that.
"But, as I said before, at the end of the day when you are a player at Man United you have to manage yourself and you have to take responsibility for your performance and your performance in a team.
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"At Man United it's winning football games. It's all about that. It's not so complicated."
Rashford scored 30 goals across all competitions last season but has netted just four times in the current campaign.
Despite the controversy, talkSPORT understands United are not looking to offload him in the summer and see him as important part of their future.
He and United will be desperate for victory on Thursday night against Wolves as they eye another top seven finish.