On-loan Arsenal striker Aneke curled in a fantastic free-kick from 20 yards after he had been fouled by Stephen Gleeson.
Leitch-Smith then calmed any nerves around Gresty Road with a cool finish in the 69th minute after MK Dons had missed a penalty.
Darren Potter stepped up after Matt Tootle had handled in his own penalty area, but Crewe goalkeeper Ben Garratt tipped the attempt around the post, while Dons midfielder Samir Carruthers hit the crossbar when the score was goalless.
"The game hinged on us being very good for 30 minutes then us losing discipline," Robinson said.
"We became too offensive, too open and too expansive. We've conceded 15 goals in the last seven games and that isn't acceptable.
"People were doing their own thing through an eagerness to do too much. We've got to be little bit more honest and open with ourselves.
"We weren't horrendous. We weren't really poor. We were just indisciplined at key moments of the game.
"That's the problem. We had more than 50 minutes to get it back after the first goal but we felt we needed to score in the first two or three minutes, when that wasn't the case.
"And when we missed the penalty there were still more than 30 minutes to go and we know how quickly games can change.
"We were just too eager and we're trying to get back in a game so quickly, rather than being calculated about it.
"But it's a good week for me as without a game, I now have time to coach."
- Sports & Recreation
- Chuks Aneke
- Matt Tootle