After Adam Johnson's 33rd minute goal put City ahead, captain Carlos Tevez missed a string of chances to leave his side hanging on through a nervous finish.
Joe Hart had to make a number of saves to keep City ahead, and the defending got desperate towards the end.
"What we didn't do was to take advantage of some good opportunities to get that second goal, which in recent games we've managed to do," the City first-team coach said.
Tevez missed a penalty only three minutes after Johnson's goal, and that would make it a much harder afternoon's work for City.
"If you can get a second goal straight away that cushion enables players to play with a bit more freedom, but we didn't take the opportunities that playing a team like Blackpool will give you," Platt added.