The Reds have work to do in the second leg of the Champions League last 16 tie against the Greek champions after falling to a tame 2-0 defeat in Athens.
But De Gea is confident that, with the right attacking approach, United can overturn that deficit and add another entry to the list of great European nights at Old Trafford.
"We know we didn’t play a good match in Greece," the goalkeeper told UEFA.com. "They were better than us and they won.
"But now there is the return leg at Old Trafford and I think that, with our fans behind us, we have to go onto the pitch and fight and attack from the first minute. By playing and pressing well, we still have a good chance.
"We will give everything we have and play a lot better than we did there. With the atmosphere and the team we have, we can succeed and hopefully reach the next round."
United manager David Moyes must also lift his players after the disappointing 3-0 Barclays Premier League defeat to Liverpool on Sunday, but De Gea believes the switch to playing in the Champions League is motivation in itself.
"They are different matches – it’s a knockout competition and you have to win the ties," said the Spaniard, who won the Europa League with Atletico Madrid in 2010.
"In those ties there are a lot of emotions involved. It takes forever for the matches to arrive and you can’t wait for them. And then you enjoy them