Stewart said the men’s team had been “turning around the season” and shown “real progress” after being nine points behind Aberdeen at one stage.
“The signings that we made in the summer are starting to really bed in and play with a degree of confidence,” Stewart added on the club’s media outlets.
“In fairness to Philippe, he said it would always take time.”
Jo Potter’s women’s side are second in the SWPL, two points off Glasgow City and Stewart praised their consistency and said they were “right up there challenging for the league title”.
Fraser Thornton also started on Monday and Stewart said the non-executive chairman would be “one step removed” from his own role.
“Day to day, I’m going to be in the club, running the club, looking after the operational matters,” Stewart said.
Clement spoke about an incident during Sunday’s League Cup final, which Rangers lost to Celtic on penalties after a 3-3 draw, when Vaclav Cerny was fouled near the edge of the box by Celtic’s Liam Scales.
A free-kick was awarded but Clement hinted Rangers could have been awarded a penalty instead.
And Stewart said: “I have spoken with the SFA to ask for an explanation of the non-awarding of a penalty in extra time. I’ll wait to hear what the SFA have to say about that.”
