Shrewsbury have been widely tipped to struggle by the bookmakers this season but they created the better chances against the Dons.
And visiting keeper David Martin made a series of fine second-half stops to twice deny John Marsden before somehow blocking a close-range effort from Aaron Wildig.
Robinson said: "We walk away from here with a point, something to build on.
"We kept a clean sheet against a side who had scored 10 goals here in their last three pre-season home games so to keep them down to nothing was a tall order.
"I thought we were the best team first half and we finished better but they had a spell at the start of the second half when they really tested us. Over the course of play, it was 60-40 to us so maybe it was a fair result."
Robinson added: "You get so many unpredictable results the first game of the season and we've got a point."