Clarke was sacked on December 14 after the Baggies were beaten 1-0 at Cardiff, their fourth straight defeat.
He left with the club lying 16th in the Barclays Premier League table, two points above the relegation zone - seven months after guiding them to an eighth-placed finish, their highest-ever in the division.
Asked after Saturday's 1-1 home draw with Hull - Albion's first match since Clarke's dismissal - about who might come in as the new permanent boss, Foster said: "I don't know - it is up to the chairman at the end of the day.
"There are quite a few names being mentioned and in all honesty some of them are top-class managers.
"I feel for Steve Clarke really, though. He is a good bloke and a good coach. I think he has just been a bit unlucky.
"Some of the results we have had have been totally not warranted. We have been a lot better value than some of the results we have been getting."
Foster came back into the West Brom team for the Hull match, in which the Baggies were overseen by caretaker boss Keith Downing, to make his first appearance since he sustained a stress fracture in his foot in August.
It meant Albion's former Tigers goalkeeper Boaz Myhill was demoted to the bench, despite having hardly put a foot wrong in his time as first choice in Foster's absence.
And Foster said of his fellow stopper: "I know he would have loved to have played.
"Bo has been doing fantastically and of course he wants to play, as do all the other players.
"But in the goalkeeping department we spend so much time together.
"I have been behind Bo when I have not been playing and even if I had not played (against Hull) I would have been supporting him 100 per cent - and I know he was doing the same for me."
Foster - who in the second half, with Hull 1-0 up, pulled off an impressive double-save to deny Tom Huddlestone and Ahmed Elmohamady - has been able to return to action quicker than he had at one point thought would be the case.
And the 30-year-old will be hoping nothing between now and next summer's World Cup hinders his chances of being selected in England's squad for the tournament.
"I spoke to Roy (Hodgson, the England boss) when I first sustained my injury," Foster said.
"It was very good of him to give me a call.
"He just gave his commiserations because it was such a freak thing.
"I think he was actually there at the game (at Everton) when I did it.
"He gave me a nice little call to say 'unlucky'.
"I spoke to the goalkeeping coach Dave Watson in between quite a few times.
"I saw him the other week when we played Norwich - we kept up to date.
"Up until a month ago they were looking at January as when I would get back to full fitness but I have progressed quicker, which is a bonus."
Manchester City's Joe Hart has been England's established number one, although he has spent some time on the bench for his club recently having been dropped after making a series of high-profile errors.
Hart made his first Premier League appearance since October in City's 4-2 win at Fulham on Saturday, and Foster said: "He is so good a goalkeeper he definitely should be playing.
"You just have to sometimes put an arm around him. (He had to) get out for a couple of weeks, then come back and crack on again.
"Joe is capable of so much.
"The mistakes were just totally out of character."