Why coping with adversity can help Everton win the FA Cup
"We need to keep strong and cope with everything that is thrown at us."
Everton have not reached an FA Cup semi-final since they last won the trophy in 1995 against Manchester United at the old Wembley.
Moyes said: "Everton have had plenty of past success in cups, it is nothing new to this club. But I accept that it has been a while since the last one.
"We have been through some tough ones. Losing at Shrewsbury and then to Oldham springs to mind.
"But this season we have had tough draws that we have won against Liverpool and Aston Villa and that has given us the incentive to keep going.
"We had the Carling Cup semi-final last season, which showed we are getting somewhere. But this would be tremendous for the fans here who have suffered a fair bit.
"The fans here have had a lot of disappointments in the past and that is something we would like to put right.
"The injuries have been dreadful, so many of them. But the players who are still going strong have shown great character, they have been asked to play out of position and do different things and they have just rolled up their sleeves and got on with it."
He added: "But too many people are talking about Wembley, but it is too presumptuous for us to start thinking that is going to happen.
"We know we will have to play well to win the quarter-final, it is another Premier League club and we know how tough that is going to be after beating Liverpool and Aston Villa.
"We know that to get to Wembley it is going to take a lot of very hard work.
"You do need luck. But we thought we were lucky when we drew Shrewsbury and then Oldham a couple of seasons later, and we lost them both.
"This week has been different. I can feel an edge from the players, I know what the fans want. We feel differently towards this game, and we must not end up with that making us anxious on the day.
"The Cup, of course, can help us in the league. We are going for a possible cup final and a high league position, so success in one breeds success in the other."
Everton expect to have midfielder Marouane Fellaini back in their starting line-up, having been nursed through recent games with a back injury.
Fellaini has only started one of Everton's last five games due to a back problem, and was only used as a late substitute at Blackburn on Wednesday as a precaution.
Louis Saha was also only risked as a second-half substitute at Ewood Park, after making his first-team return against West Brom last weekend having been out since November with a hamstring problem. He too, should start.