Foster was forced off 12 minutes from full time with an ankle injury during the Baggies' goalless draw at Everton in the Barclays Premier League.
The 32-year-old had otherwise been in superb form, producing a number of fine saves to preserve a clean sheet in front of watching England manager Roy Hodgson.
Clarke said: "In his own words, he felt a pop in his ankle. He said the pain was obviously strong.
"Ben is not the type of guy to go down if there is nothing wrong.
"The fact he went off the pitch tells you it is an injury we have to be a little bit worried about.
"At the moment until it is diagnosed we will let the medical people do their job and have a look at the scans.
"It is difficult to say what the prognosis is or the outcome.
It is best to say it is just an injury that worries me."
With Boaz Myhill also injured, third choice Luke Daniels played out the closing minutes and although lucky with Marouane Fellaini and Seamus Coleman hitting the woodwork, he also held firm.
Everton created the better chances throughout the game but Clarke felt his team deserved a point, their first of the season, for their resilience.
He said: "Ben was excellent today as were the rest of our team.
"Our season started today. Last weekend was disappointing. We were determined to come here and address today what we didn't do last week."
Clarke felt preparations for the game had gone well despite the disruption of losing Nicolas Anelka in sad circumstances.
Summer signing Anelka has been granted indefinite compassionate leave following the death of his agent.
Clarke said: "The actual preparation has been okay.
"Nicolas had been injured anyway so he hadn't trained.
"The team I started with was the team I worked with for three days last week. It didn't disrupt us for preparation."
There have been suggestions veteran striker Anelka is considering retirement but Clarke intends to give the player time to think carefully about the situation.
He said: "We will wait until Nicolas indicates to us he wants to sit down and have a chat. That is the best way."
Everton were frustrated not to have claimed their first victory of the season after also being held to a draw at Norwich.
Manager Roberto Martinez was still encouraged by the performance.
The Spaniard said: "We knew it was going to be a really tough game. It was a really hard fought game for both teams.
"West Brom came with intent to keep a clean sheet.
"I was very happy with what we did off the ball. We suffocated West Brom and Tim Howard only had a couple of saves.
"It was just getting that goal. I think we did enough to get the three points but the ball was bouncing in and bouncing out, that was the difference today."