Bamford could have opened the scoring for the hosts even earlier than that after sending an effort on to the crossbar while Ryan Colclough almost equalised late on.
While Crewe are still searching for a win this season, Dons - who drew at Shrewsbury on the opening day - are now two unbeaten, while the victory follows their midweek win over Northampton in the Capital One Cup.
Boss Robinson said: "I thought first half we were sensational, it was a wonderful performance and we could have been two or three in front without any arguments.
"But second half we had a 30-minute spell where I thought we were poor - diabolical to an extent. We were lethargic, which is not like us, and that allowed them into it.
"But it has been a good week - two wins and a draw including a local derby win and winning our first home game of the season.
"I don't think as a manager I can ask for too much more than that. I thought the energy in the first half was sensational.
"But second half they showed their youthfulness with their lethargy in the final third. Rather than killing the game off in the first 15 minutes we let them back into it."
Robinson continued: "We've got a number of Premier League and ex-Premier League players and I think collectively as a group they're very talented.
"I honestly believe we've got a long way to go with these young players but they've done a wonderful job over the last few games.
"Two clean sheets in two league games says it all about the way we are defending."
- Sports & Recreation
- Patrick Bamford
- Ryan Colclough
- Jason Banton