Mark Hughes felt Stoke's professionalism ensured they were never going to be on the wrong end of a cup upset against Rochdale.
The Stoke manager made eight changes for the Carabao Cup second-round tie against the League One side but it was still a strong team containing the likes of Kurt Zouma, Bruno Martins Indi, Joe Allen, Bojan and Peter Crouch.
Two goals from Allen, captain for the night, either side of a Crouch strike meant the tie was all but over before half-time. Ramadan Sobhi completed the scoring late on with his first goal for the Premier League club.
"We have all been involved in these sort of games throughout our careers whereby when the match hasn't been approached in the correct manner then it has turned into a difficult 90 minutes or so," said Hughes.
"If you take liberties with any level of opposition then you can come unstuck, but thankfully our guys, to a man, showed great professionalism this evening.
"We didn't want to allow them to gain any momentum and enjoy themselves and we never had any moments of real anxiety to be perfectly honest."
The manner in which Stoke approached the tie was also not lost on Rochdale boss Keith Hill.
He said: "If you're going to get a cup upset it's generally down to the opposition fielding a weakened side and not fancying it, Stoke fancied it.
"They are an excellent side and I love the way they play. Some of Charlie Adam's passing was sublime. But f or three of the four goals we had the ball and gave it away, so we were a bit naive."
Stoke travel to Ashton Gate to play Bristol City in the third round. The Robins have already accounted for a Premier League scalp in the shape of Watford, having won 3-2 at Vicarage Road on Tuesday night.