United have conceded seven goals in their last two matches, to Saints and Kilmarnock, and have scored seven times to get away with two points in the league.
Without Webster's calming influence the Tangerines' defence has looked shaky, but Houston has spent hours on the training field this week trying to rectify the problems.
Darren Dods and Garry Kenneth will be the central defensive partnership and Houston insists he has full confidence in his back four.
He said: "Andy has suffered a bit of a reaction so I'd have to say he's extremely doubtful for Saturday's game.
"It's disappointing because we hoped to have him available but we've got three quality centre-halves so I've got every confidence in the guys who will play.
"Andy has been doing training with the physio but he's felt a niggle from it. Calf injuries are difficult ones to deal with and the last thing we want to do is rush him.
"We have a game on Wednesday and then the following Saturday so we don't want to push him.
"We've worked hard on our defending this week and we've been focusing on how we deal with corners.
"I've had the players round the houses in that respect so we should be able to deal with what St Johnstone throw at us.
"Obviously when we score seven goals in two matches we don't expect to lose seven at the same time.
"But that's done now, we have a new 90 minutes to look forward to and the lads are desperate to get going."
United expect to take more than 4,000 fans to McDiarmid Park this weekend and Houston insists the supporters can play an important role.
United have a poor recent record in the competition but are fully focused on rectifying it this season.
"Since I've been at the club the fans have really turned out for the Scottish Cup," Houston added.
"I remember against Inverness a couple of years ago they went up there in great numbers, some of them were dressed up and it was a real day out for them.
"Then against Hamilton last year we took a great crowd as well. So with St Johnstone just being down the road I'd like to think we'll have a big following.
"The supporters have been brilliant with the players this season and their support is important. But I know from experience never to look too far ahead in cup competition.
"St Johnstone are an established SPL side, they have recorded some great results this season and of course they beat us in the League Cup down there.
"So while it's great for fans to think about going on cup runs, everyone involved on the playing side is just looking towards this weekend's match and trying to get through it."