Yes, sometimes a better position worths more than a pawn, but I'm not sure this is the case. My big mistake was allowing your knight to eat my knight in the 6th movement. Since then I have an inconfortable position. Let's see what happens ...
1. e4 e5
2. Nf3 Nc6
3. d4 dxe4
4. Nxe4 Nf6
5. Nc3 d6
6. Nxc6 bxc6
7. Bc4 Be6
8. Bxe6 fxe6
9. O-O d5
10. ed cxd
11. Qe2 Qd7
12. Re1 Kf7
13. Bg5 Bb4