No. Taking the knight is a forced loss for black.
2...f6 is not very good, it takes away the best square for your knight and exposes your king. The f pawns are the weakest point in the initial position (only guarded by the king) and also serve as a shield to the king after 0-0 (castling kingside is faster than queenside) so we get the general advice to not move the f pawn in the opening. When you do, it's often two squares forward to keep the f6 square clear for a knight (or f3 when you're white).
All that said, if you really do want to play 2...f6 here, you can, but you can't take the knight.
A very solid defense is instead 2...d6
Is there a way that I can beat this? I want to keep the knight that is sacrificed, and avoid losing my rook in the process. The only way I've gotten past this is to not take that tasty knight that is offered up. Suggestions? (I play as black):