The two sides meet at the Donbass Arena in the Champions League tonight having both won their Group A openers.
However, the former Arsenal forward believes that recent success against English opposition will work in Shakhtar's favour.
"We have the opportunity to win this game," Eduardo told The Sun. "United may be in trouble but they are still strong and we have to concentrate.
"But they will be under pressure even if the teams have a different mentality in the Champions League and raise their game.
"We beat Arsenal here a few years ago and Chelsea last season. We always play very well at home."
The match gets underway at 7.45pm.