Wednesday's game at Hampden could provide Webster with the opportunity to earn his first cap since March 2006 after he was one of three United players called up to the squad for Craig Levein's first game in charge.
The player will now be assessed by Scotland medical staff before a final decision is made on his fitness.
Houston - who is also Levein's number two with the national team - said: "Andy's other calf was sore from training on Thursday and it was touch and go whether he played today.
"The biggest concern for me is that I don't want him out for four weeks. It's getting better but he still felt a twinge.
"He will go to the Scotland squad and be assessed. I phoned Craig and let him know what was going on last night.
"The biggest thing for me is that he's all right for Hearts next week. Craig is aware of the situation.
"I'm not a medical guy. He will probably train on Monday but, if he's feeling it at all, I think Craig will just keep him out. It is getting better and maybe by Monday or Tuesday it will be better again."
David Goodwillie set the ball rolling in the win over rock-bottom Falkirk when he converted from the penalty spot, before Morgaro Gomis claimed a double.
The victory - combined with Hibernian's draw with St Johnstone - allowed the Tangerines to overtake Hibs and go third but Houston refused to read too much into their lofty position.
He said: "People have spoken about us being third but that doesn't really matter to me just now.
"If we are third on the last day of the season, I'll be absolutely delighted. I just feel there are a lot of games to go, a lot of hard games, and there are no easy games in the SPL.
"But it's nice that we're still challenging up there and we are ahead of our schedule. We are improving every year and on schedule to do that again."
Houston singled out Scotland Under-21 youngster Goodwillie for praise, adding: "He's a talent and he could have scored more today.
"He has been playing with a groin injury he just can't get rid of and I've got plenty of praise for the lad, he just battles on regardless and I'm really pleased with him.
"To score as many goals as he does in the SPL for a young boy is great. He had his troubles earlier in the season but he doesn't want to talk to press or TV guys, he just wants to knuckle down and he is scoring goals."
Despite the result, Bairns boss Steven Pressley had nothing but praise for his players.
He said: "It was a disappointing result but a terrific performance. I couldn't have asked for any more from each and every one of those players today.
"How we lost the game 3-0 is beyond me because I thought we were excellent.
"The penalty changed the game and I'm not convinced it was a penalty. I also thought we were unfortunate ourselves not to get two penalties."
Source: Team Talk