Foster limped off on 78 minutes and had to be replaced by Luke Daniels.
Foster, who had recently come out of international retirement and played in a friendly against Ireland in May, was in inspired form until that point to keep Everton at bay.
"It's obviously serious as he had to come off during the game and Ben is not the type of person to come off unless he has to," Clarke said on the BBC.
"He said he felt something pop in his foot and said he was in a lot of pain. But until the medics look at it, it's only conjecture as to what the problem is.
"It was great for Luke to come on and I had no worries about him as I see him every day in training. It shows if you are patient you get your chances."
Clarke was pleased with his team's resilience to pick up their first point of the season after they lost their opener 1-0 to Southampton last week.
"It was a good point and a hard-earned one. It's nice to see West Brom back and the first game was disappointing, but we bounced back very well," Clarke said.
"Everton are a good team, but we showed that as well. The goals will come and we showed we are a team that create chances. But today was about digging in and getting a good result."
(Reporting by Toby Davis; editing by Stephen Wood)
