United are bottom of Group A and will be eliminated if they lose in Turkey in their penultimate group fixture on Wednesday.
Even if they beat Galatasaray and defeat group winners Bayern Munich at Old Trafford in their final game, two wins for Copenhagen would send the Danish side through instead of Ten Hag's team.
United, three-time European champions, have never won at Galatasaray - drawing twice and losing once.
They were famously greeted by Turkish fans in 1993 holding a banner that read "Welcome to Hell", while others threw missiles and menacingly drew their fingers across their throats.
That game finished in a 0-0 draw, which sent United crashing out of Europe on the away goals rule after a 3-3 draw in the first leg.
Speaking at a pre-match press conference on Tuesday, Ten Hag insisted his men would travel with confidence despite their predicament and the hostile reception awaiting them in Istanbul.
"We know how to deal with it and I'm sure tomorrow it will be a confident team on the pitch," said the Dutch manager.
"You have to stay calm in your head and don't get too emotional. You need emotion but you have to control it. Don't give them anything, or the referee as well.
"You have to stay away from such moments. We know how to deal with it. You have to play confident and you have to make it your game so it's not that important how the opponent is playing, it's important how we are playing."
Ten Hag said United had improved since their shock 3-2 defeat to Galatasaray at Old Trafford early last month despite their inconsistent results this season.
They beat Everton 3-0 on Sunday to record their fifth Premier League win in six games.
"It's good progress," he said. "We are stepping up, we are more stable, we are winning games, so definitely there is a big difference from the first time we played them."
'Intense' atmosphere
United captain Bruno Fernandes said he was looking forward to playing in Galatasaray's "intense" atmosphere.
"The atmosphere will be intense but I think everyone, as a kid, you enjoy and you want to be in these big stadiums with a big atmosphere so you just have to enjoy the challenge," he said.
Well aware of the prestige that comes from playing in Europe's elite club competition, Fernandes acknowledged the importance of United avoiding elimination on Wednesday.
"It's really important to be in the competition, we want to be in the middle of the best clubs in Europe," the Portugal midfielder said.
"It's disappointing if we don't go through but I'm not thinking about that at the moment.
"I'm just focused on the game against Galatasaray because the only way we can go through is winning against Galatasaray and going to the last game with a chance to go through."
Rasmus Hojlund and Antony are in the squad after recovering from injuries, providing attacking options for a United side that will be without Marcus Rashford due to suspension.
