The former Scotland assistant recently confirmed he would not be renewing his contract when it ended in the summer, citing further cutbacks at the club, combined with his own desire to progress as a manager, as the motivating factors.
However, after days of speculation as to who would be his successor, with Falkirk manager Steven Pressley and Partick Thistle boss Jackie McNamara among the front runners, United this morning announced that Houston had left the club by mutual consent.
McCall, though, expects the usual tough test against the Taysiders, regardless of who or who is not in their dugout.
"There will be no Peter there and obviously I wish him all the best, I think he did a terrific job there," McCall told Press Association Sport.
"I doubt whether the new manager will be in place but one thing about Dundee United is that they have an experienced squad.
"They have good pros in that dressing room like (Jon) Daly, (Sean) Dillon, (Willo) Flood and (John) Rankin and regardless of who is taking the team, whether the new manager is to be is up in the stand or whether he won't be announced by then, once you are out on the pitch you do your best to win football games.
"I'm sure a lot of them will be disappointed to see Peter go but they knew it was going to happen sometime.
"We just have to concentrate on ourselves.
"It is two evenly-matched sides, so it will be about on the night, who deals with the conditions and takes the chances when they come up."