I feel the recoil from my Savage .308 when I'm on the bench rest, practicing my shots. But it's not that bad.
When I got my 5 pointer up in New York on my sister's farm, I never felt the recoil at all. I just remember myself trying to stay calm, focusing hard and keeping the crosshairs steady on the buck. I gently pulled the trigger and BAM! I dropped the buck in his tracks.