The striker was brought off after just 22 minutes after going down after taking a knock to his shin.
Madine was evidently unhappy to come off as he remonstrated with Appleton in the dugout while Theo Corbeanu replaced him.
While the two eventually shaked hands, they continued to exchange words before Madine eventually took his seat on the bench.
“He was just frustrated,” Appleton told The Gazette.
“But the reality is, he’s been limping around for five minutes and we were playing with 10 men, so unless the physio is going to bring the magic sponge on like you do in the Sunday League…
“It was definitely the right thing to do.”
The withdrawal of Madine saw Jerry Yates move over from the left wing into a more central position, while Corbeanu took his spot out wide.
The two were unable to stop Blackpool from slumping to their first defeat of the season as goals in either half from Harry Clarke and Jacob Brown handed Stoke a deserved three points.
When asked for a prognosis on Madine’s knock, Appleton added: “I’m not sure at the minute.
“He got a kick to the shin, which is a blow because he’s done well for us in pre-season and he did well for us (against Reading) last week.
“It doesn’t help, but we have got players in the squad who can come in and do the business as well as Jerry showed to be fair, because when he went into that central position he looked quite lively.”
Appleton’s men produced a lacklustre display in their first away trip of the campaign and can have no complaints with the final result.
The Seasiders played Stoke far too much respect at times, especially during a drab first-half where they only invited pressure on themselves.
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.