Houston decided last week to part company with United when his contract expires in the summer, but his players responded well to the news with a 3-2 victory at Kilmarnock on Saturday.
Mjallby is confident the Tannadice men will be equally committed when they travel to Celtic Park on Tuesday night, and for the rest of the season, as they will not be too concerned with matters outside the team.
"It doesn't really matter because the players are going to be professional anyway," the Swede said.
"They have to think about their places because even if they know that Peter is not going to be there next season, there might be someone that knows he is going to become the manager and is looking at the team all the time.
"They need to perform and do as well as possible. I don't expect anything other than a good performance from them."
Mjallby expects another tough encounter with United and he believes Celtic will have to be wary of Jon Daly and Gary Mackay-Steven as well as Johnny Russell, who scored a hat-trick in that Rugby Park win.
"They are very, very good," Mjallby added. "They are a wee bit different, all of them, which is handy for Dundee United.
"Jon Daly is strong, a bit of an old-fashioned striker, very good in the air. Johnny is very nippy, with good movement, and can score goals. Gary Mackay-Steven is more of a winger and very good one v one."