It looks like you played well and thought things through, but just didn't see the Nb5 in-between move coming to add another defender to e5. I'd still consider this falling for a tactic, or you could say you didn't calculate well enough to anticipate this. It happens. Literally. This kind of thing happens to everyone.
On a bad day (or grinding chess by pulling an all-nighter), I could see myself falling for something like this, but assuming the player (myself or anyone else) is in decent form, then this is maybe 1800 chess.com rapid level tactic I'd say. The Nb5 was the unexpected shot which makes this entire thing work, but other than the potential surprise value, this was fairly straight-forward to calculate.
The subtle 1800+ or even 2000+ observation (which both players seemed to miss) was the opportunity to go after the bishop pair. Move 14. a3 was okay by the opponent, but notice that the top engine move in the post-game analysis is 14. Nh4 to threaten winning the bishop pair. If it wasn't for your queen under attack with Nb5, then your e5 knight would be attacking their c4 bishop (threatening to win their bishop pair). If you changed the move order of captures, you can play: 13...Nc6 14. a3 Ndxe5 15. Nxe5 Qxe5! when them trading queens is suboptimal due to 16. Qxe5 Nxe5 and your centralized knight is attacking their bishop.
For a little bit of importance about the bishop pair, this video of mine might help you 
So, in the above position, I play 13...Nc6 attacking e5 and b4, and I even had previously moved the N to e7 to have this opportunity. My opponent plays 14.a3. I take on e5, via 14...Ndxe5, which apparently is already a mistake, because after 15.Nxe5 Nxe5, we get 16.Nb5, and 16...axb5 fails to 17.Bxe5, after which, for example, 17...Qe7 is no good, and nothing else works either.
It seems almost pointless to try to "play well" when you can set up winning a pawn, clearing a square for development of your last piece, enabling future castling, and sorry, no, there's a 7+ ply tactic that loses, which seems non-obvious even after I've written this post.
Anyway, what level of player expects to see this in time to avoid it?