Albion picked up their first league win of the season against Sunderland on Saturday and Clarke is hoping to see his squad maintain that form.
They face Arsenal – a side they have not beaten in three years – and although Arsene Wenger is expected to use some of the younger players in his squad, Clarke still has the visitors as favourites to progress.
"We can be dangerous underdogs," he told the club's official website. "As a team the last two performances have been good.
"Arsenal at home is a difficult game – it’s a good game.
"I’ve got a nice squad of players who all want to play. It's up to me to get the right mix on the pitch on Wednesday.
"I've got players who need to play and players who want to play.
"Hopefully winning on Wednesday night and progressing in the cup will be good for the squad, because we have a big squad, so the longer you stay in the cup competitions the better."
One player who will be pushing for a start is young striker Saido Berahino, who netted a hat-trick in the second-round win against Newport County.
Arsenal have triumphed on their last four visits to the Hawthorns and will be confident going into the tie after their victories over Marseille and Stoke in the last week.
Wenger has generally used the League Cup to introduce some of his young players, which means the likes of Emmanuel Frimpong, Serge Gnabry and Chuba Akpom could start.
One youngster who will not be involved is Gedion Zelalem after the midfielder was ruled out for two months earlier in September.
He is joined on the sidelines by Santi Cazorla (ankle), Abou Diaby (knee), Alex Oxlade-Chamberlain (knee), Lukas Podolski (hamstring), Tomas Rosicky (thigh), Yaya Sanogo (back) and Theo Walcott (hip) as the injuries begin to mount for Wenger.
West Brom have fewer concerns, although they are without some important members of their squad.
Chris Brunt (groin), Ben Foster (foot) and Shane Long (hamstring) will all be missing for Albion, while Steven Reid (knock). Matej Vydra (hamstring) and George Thorne (knee) are doubtful for the clash.
