The American was dismissed on Monday following a run of seven league games without a win, with Leeds only outside the relegation zone on goal difference.
United's only loss in their past 15 matches in all competitions came against Premier League leaders Arsenal.
But before the start of that run Ten Hag's men were beaten by Aston Villa in Unai Emery's first game in charge.
"We have to be aware of that," Ten Hag said on Tuesday. "When Jesse Marsch was in the lead, it was clear how they play. Now it's possible they change -- it's also possible they don't change. I think we only will find out on the pitch tomorrow.
"But then we need good anticipation of that. The difference at that time (against Villa) was when Emery came in they had a week, or maybe even longer, to prepare. And now they have not so much time to prepare."
Wednesday's match at Old Trafford will be the first of two games in five days between the traditional rivals, with United travelling to Leeds on Sunday.
"It's definitely a big game in this part of England and it's a big game for us," said Ten Hag.
"We have Man City, we have Liverpool, but as well for our fans this game means so much and our players are aware of that and they know what to do."
Ten Hag will be without Casemiro for the next three games after the midfielder was sent off during the 2-1 win against Crystal Palace at the weekend.
Casemiro's absence could mean a first start for Marcel Sabitzer, who made his debut as a substitute against Palace following his loan move from Bayern Munich.
Leeds interim boss Michael Skubala, speaking at his own pre-match press conference, said work was well under way to find a replacement for Marsch, with Rayo Vallecano's Andoni Iraola understood to be among the candidates.
West Brom head coach Carlos Corberan, who worked under former manager Marcelo Bielsa at Elland Road, remains the favourite for the job.
"I think it's every coach's dream," Skubala said. "I'll be up for this as much as the other players and coaching staff. It's very exciting.
"We have a good staff team. We have 24 hours. We have one session this afternoon that we've prepared.
"I think there may be a few little tweaks and differences, but we have to make sure players understand the game plan. We can't be passive, but we need to be pragmatic."