Goals in either half from Harry Clarke and Jacob Brown handed the Potters a deserved victory against a below-par Blackpool side.
The Seasiders played Stoke far too much respect at times, especially during a drab first-half where they only invited pressure on themselves.
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While the away side did improve slightly in the second period, it was nowhere near enough to get a result.
Defensively Blackpool were poor, with both goals coming via left-wing crosses. In attack, meanwhile, they were far too reliant on Josh Bowler to create anything of note.
But as for Stoke, O’Neill was delighted with how his side bounced back from their opening day defeat to Millwall.
“I think we played with real composure today and had real control, particularly in the first half,” he said.
“We didn’t panic, we passed the ball extremely well and were patient.
“We could have gone ahead before we did, scored a brilliant goal involving both wing backs with a cross from the left from Josh Tymon and a great header from Harry at the back post.
“Then I thought we created good chances in the second half.
“Blackpool came into the game a little bit more which we expected, but I thought we defended well and looked a lot more composed.
“There was more self-belief in the team than I think we showed against Millwall last week.
“You are always hoping for a reaction to a defeat. We asked the players today to give us a performance and they certainly did that.”