Bamford scored a stunning late goal to spare the Dons' blushes after the 10-man Millers had battled back from two goals down to equalise.
Robinson said: "I thought we were very good, apart from the two suicidal goals we conceded.
"Last year we would have drawn that, but we showed grit and determination to go on and win it - you can see by the way they celebrated that goal it's a team that's together.
"Patrick is just unbelievable. I'm just enjoying working with him, I feel very lucky.
"The dialogue between us and Chelsea is constant - they really care for the boy, they see a future for him.
"If you're a Chelsea fan you've got a special footballer waiting to come and grace your pitch.
"His path at Chelsea is nothing to do with us, but all we can do is make him a better footballer while he's here.
"Chelsea know where we sit with it, how many times can I ask them if we can keep him?
"He's happy here, he's getting better and he'll get better by playing more games and scoring 30 goals in a season - me and him have had a little joke about a target for him."
Rotherham Evans was sent to the stands at half-time for an incident in the tunnel.
Shaun Williams put the Dons ahead on the stroke of half-time when his low spot-kick squirmed underneath Scott Shearer after Michael O'Connor had been sent off for tripping Stephen Gleeson.
Ben Reeves doubled the Dons' lead in the 65th minute, but Rotherham scored twice in as many minutes to make it 2-2, through Lee Frecklington and Tom Flanagan's own goal.
But Bamford swept the ball into the top corner from 20 yards in the closing stages to snatch the points for the Dons.