Villa head into Saturday's third round clash with League One Sheffield United having moved six points clear of the relegation zone courtesy of the 1-0 New Year's Day victory at Sunderland.
And when asked if his fellow top-flight managers would prefer to avoid the FA Cup altogether, Lambert said: "If they were being honest, they probably would do. 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.
"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.
"We don't have a massive squad and points are really important. If you are honest enough people will say the same."
Villa's options have diminished with news striker Libor Kozak has been ruled out for the rest of the season after suffering a broken leg.
The 24-year-old Czech Republic international will undergo surgery on Friday after he was injured in training.
Villa issued a brief statement on their website to confirm the injury, adding: "Regretfully, he will play no further part this season."
Kozak joined Villa from Lazio in the summer for £7m and has started eight Premier League games this season as well as making six appearances from the substitutes' bench, the last of them in the 1-1 draw with Swansea City on December 28.
He has netted four goals for Villa so far and his loss is likely to force Villa manager Paul Lambert to move for a new striker during the January transfer window.
Lambert does have Christian Benteke available again now, however, after the Belgian forward returned from a calf injury to partner Gabriel Agbonlahor up front in the 1-0 win at Sunderland on New Year's Day.