Onana, after a difficult few weeks, kept a clean sheet for United in victory at Burnley last night.
Robinson told BBC Sport: "Andre Onana has had a difficult start at United. He is playing in a team that is underperforming and conceding goals.
"He has come in as a very expensive goalkeeper, almost £50 million and he is expected to hit the ground running and play well.
"He got away with a potential penalty in the first game of the season against Wolves and his form has struggled.
"We speak often about the weight of the Man United shirt and many have crumbled under it, and the pressure at Old Trafford is immense."