Late strikes from Said Benrahma and Emiliano Marcondes gave the Bees a 2-0 success in Saturday's lunch-time kick-off at Craven Cottage that hauled fourth-placed Brentford to within a point of third-placed Fulham.
The victory still left Brentford seven points behind second-placed West Brom and eight behind front-runners Leeds United ahead of their weekend games but Frank said his side at least maintained prospects of challenging for a top two finish, especially with the Baggies visiting Griffin Park next Friday night.
"There was nine games left of the season and we have a big ambition to see if we can get promoted," Frank told Sky Sports.
"Of course if you are up there where we are now, of course you need to go for that.
"And why not go for the top two?
"But I have also been saying the whole season, one training at a time, one game at a time and we can't do that differently now.
"Of course we knew that this game and the next game was extremely important but obviously if we didn't win today then the next game doesn't matter more or less for the top two.
"So now we have a chance and we are ready to meet West Brom next Friday."
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