"I think if you asked the majority of them, if they were being honest, they probably would do," he said. "Not just because of the money but survival in the league is vital.
"It is realistic. That is the nature of it. If anyone says any differently then I am not so sure they will be telling the truth because the Premier League is the most vital thing that anyone wants to get into and we are no different."
Lambert's side are in 11th place in the league, six points above the relegation zone, and the Scot made it clear that his priority is staying up and not the visit of third tier United.
"Cup competitions, if you can get through, then absolutely I want to get through. I don't want to not get through, but your main one is the league," he said.
"We don't have a massive squad and points are really important. If you are honest enough people will say the same."
Villa's last FA Cup triumph was in 1957 and they have not reached the final since 2000.
Last term, Wigan Athletic became the first team to win the trophy and be relegated from the top flight in the same season.
(This story has been refiled to amends headline, no change to text)
(Writing by Ken Ferris; Editing by Greg Stutchbury)
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