You should be adding the Eb resonance key to that note, as that does help bring up the pitch and match tone color.
Like Mikhail said though, the primary reason this was an issue on one of my bassoons was that the A tone hole (the one that gets covered when you engage the G key) doesn't open the correct amount. It might not be as serious as the tone hole being clogged, but it could simply be the pad doesn't come up enough. The easiest way to let the pad open more is to shorten the plastic rod that connects the touch to the pad, the rod that goes through the boot joint. Remember though that if you cut the rod you can't put it back, so take it to a good bassoon repair person that can see if that is truly the adjustment that needs to be made, and can make the right adjustment for you.
If you want to try it yourself though you can take a coffee stirring straw (the little skinny kind) and cut it to the length of the rod as it is, then cut it a little bit shorter. Place that in your horn instead of the stock rod and see if it helps the problem. If you find that making it a bit shorter corrects the issue you can make a more permanent change to the original plastic rod. Be sure to check not only the F you're having problems with, but also the two A's below that, as well as C#, as that can become unstable with adjustment to this tone hole. When in doubt, go to a competent repair person.
For me on my old instrument it was the opposite problem, the pad opened too much, leading to relatively sharp F4, A3 and A4 and an unstable C# in the staff. Adding cork to make the tone hole less open when the touch was not engaged helped the problem immensely.
M.M.A., D.M.A. University of Illinois at Urbana/Champaign: B.Mus. Lawrence University
Bassoon professor at University of Wisconsin Eau-Claire
Maker of the Little-Jake electric bassoon pickup and Weasel bassoon reeds