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 today 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.
"They come at you and attack you. They give you respect but they do that by taking the game to you. That leaves room for you to create and exploit but it also leaves you on a knife edge because they can get a goal.
"We were definitely the happier team to hear the final whistle."
Tevez also missed an open goal as he fell after rounding the goalkeeper, but Platt says the Argentinian should not be too downhearted.
"Things tend to balance out for strikers and for teams," he said.
"If you create that many chances and only get one goal, hopefully in the next one you might only create a few but get two or three goals.
"The most disappointing thing for a striker is when you don't get any chances but today he had eight or nine and if he keeps going like that the goals will come."
For Blackpool, the disappointment of defeat was tempered by another strong display from a team that continues to defy all pre-season predictions.
"We threw just about everything we had at them, which I wasn't sure we were going to do in the first half," manager Ian Holloway said.
"We looked a bit hesitant early on, and we don't normally look like that, but maybe it was a hangover from the other times we've played away against one of the top teams and got a bit of a pasting.
"I think putting Matty Phillips on at half-time gave us some hope and some belief because he's not scared of anything.
"He ran with it and turned someone inside out who got taken off straight away. Then he did it to the new bloke and I wondered if they had any more left-backs.
"But we put another centre-forward up front and I put all my strikers on and we couldn't have been more positive if we tried, but unfortunately we're on the bus home with our tails between our legs."
But Holloway was horrified by the defending for City's goal.
"We've gone and lost to a horrendous goal from my point of view and from my team's point of view," he said.
"You win a header from a corner and it falls to someone who shoots from the edge of the area and no one blocks it. We were a bit statuesque."
While Holloway did not argue that Luke Varney fouled Yaya Toure for the penalty, he disputed the decision to give City a throw-in from which the incident stemmed.
"I'm delighted they missed the penalty because it was a throw-in to us," he said.
"It was a penalty, but that was a throw-in to us, I can't stress it enough, I was stood right there. Our throw-in."
But even with today's defeat, Blackpool start 2011 in the top half of the table and with games in hand after recent postponements, giving Holloway much to be happy about.
"I don't think we needed much improvement to get a result today, so that is what encourages me in all of this," he said.