Stubbs has agreed terms with Rotherham United and could be announced as the club's next manager on Wednesday.
"I would just like to think the work that Alan Stubbs has laid down, that any incoming manager goes along the same lines," Stanton told BBC Scotland.
"Because it was certainly proving a success for Hibs."
Stubbs inherited a threadbare and disconsolate squad at Easter Road following the blow of relegation in 2014.
The former Everton and Celtic defender failed to return the club to Scotland's top-flight in his two seasons in charge, finishing second, then third, and losing at the play-off semi-final stage each time.
However, after guiding the Easter Road side to the League Cup final in March, where they were beaten by Ross County, Stubbs delivered the Edinburgh club's first Scottish Cup triumph since 1902.
"I suppose I'm disappointed that he's leaving but also good luck to him," said 71-year-old Stanton, who played for the club between 1963 and 1976.
"Hibs were going nowhere, and he's come along and turned the whole thing round.
"It took him a wee while, I know this season was disappointing towards the end of the league, but we were in two cup finals and progressing in the right way.
"I think he's done very well, he conducts himself well. He's a player's man, but they've got to get on with their side of things as well.
"There'll be another manager appointed shortly and they'll just need to get on with him."
The rebuilding undertaken at Hibernian under Alan Stubbs must not be squandered if the head coach departs, according to club legend Pat Stanton.