Pilley sprung a surprise move in sacking Micky Mellon following the Cod Army's 3-2 defeat to Aldershot in the FA Cup last weekend, despite them lying in the League Two play-off places ahead of Saturday's match with fellow promotion-hopefuls Southend.
"No, not at all," said Pilley when asked whether Alexander had been set any goals upon penning a rolling contract at the Highbury Stadium. "I want the football club to progress but I am realistic, I live in the real world.
"He picks up a squad which is not his own. He's got to establish the abilities of the players, he's got to stamp his own identity onto the squad.
"Eventually, over time I have no doubt the squad will become the Graham Alexander squad and, given time, I'm sure the club will continue to progress and continue to be a success under Graham."
Pilley admitted he was happy to draw a line under a rare unseemly chapter in Fleetwood's meteoric rise from non-league obscurity.
"It's been hectic, it's been stressful because I care greatly about the football club," he said.
"It's been a time whereby we've had to do everything we can to ensure we make the right decision.
"We've been incredibly busy - I've hardly seen my family, the truth be known. I've not travelled anywhere, that's just a reflection of the hours we've put in.
"But we're convinced we've made the right decision and we're looking forward to a really exciting future with Graham.