Asked how big the task ahead was, Dyche said at his pre-match press conference on Wednesday: "Certainly a decent-sized one.
"They'll be favourites of course after the scoreline over there. We have a few challenges with injuries, a pretty low squad at the moment.
"But we've been productive before when the challenge is against us, so obviously that is what we are looking to do.
"I think they (the Burnley fans) will be very important. I think there will be good numbers. I think they believe the tie is still alive, as we do."
The first half of leg one saw Burnley striker Chris Wood's penalty cancel out Kostas Fortounis' opener and Olympiakos had some enthusiastic penalty appeals rejected by referee Slavko Vincic.
The hosts went 2-1 up through Andreas Bouchalakis soon after the break and then added another goal on the hour when Ben Gibson was judged to have been guilty of handball in the box by Vincic, who showed him a second yellow card, and Fortounis converted the resulting penalty.
Dyche afterwards questioned Vincic's decision-making in that moment, and claimed that at half-time "all and sundry" from Olympiakos had spoken to the referee in the tunnel, "making it clear they weren't happy" with his performance.
Dyche said on Wednesday: "Whatever happened in the last game, it's a fresh game, a new start, a bigger challenge, obviously, with the scoreline. The away goal is helpful. It would have been nicer if it wasn't the scoreline it is, but it's another challenge for us.
"I said my piece over there. I made it clear I was trying to be concise about facts rather than getting too emotional. So we focus on this game and see what we get from it."
United lost 3-0 at home against Tottenham on Monday, and when asked about the criticism Red Devils boss Jose Mourinho has faced, Dyche said: "It's part of the job - he knows that. Win or lose, there's always someone not happy with what you are doing.
"I remind myself of these managers' records. It's unquestionable for me - there's no doubt he's a top manager. His own challenge will be his own. That will be for him and their football club to work through. It's certainly none of my business."
Dyche was also asked if he had one eye on the United game while preparing for Thursday, and said: "I think we have got to in reality, but it's only one eye.
"We've made it clear to the players that the next game is the most important. We don't want to overthink the one after that. But of course, we have to be aware - it's Man United, a fantastic football club and a big challenge."
Dyche also confirmed that as well as defender Gibson, suspended after his dismissal, Burnley on Thursday will be without winger Johann Berg Gudmundsson, who came off in Sunday's 4-2 loss at Fulham due a hamstring problem.