Cole's goal at the Keepmoat Stadium within the first minute of the game helped to secure a second league win on the trot for Parkinson's men following the success at Rochdale a fortnight earlier.
The goal was Cole's fifth of the season already but it was the work-rate shown by the striker to help get the Bantams over the line that equally impressed the City chief.
Parkinson said: "I thought his work in the second half in particular for the team was immense.
"I said to him at half time 'Go out and get another goal but if you can't, make sure your first goal helps to win us the game'.
"The manner in which he closed down Doncaster's centre halves in the second half was tremendous.
"He looked to get tight to them and try to rob the ball off them. He was certainly the first line of defence for us."