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.
Nicklas Bendtner is set for his first Arsenal appearance since August 2011 against West Brom.
Arsene Wenger will rest some of his key players, including Jack Wilshere, while Theo Walcott needs stomach surgery.
West Brom's second-round hat-trick hero Saido Berahino is pushing for a start, having come off the bench in Saturday's win over Sunderland.
His cause will be strengthened by the expected absence of injured strikers Shane Long and Matej Vydra.
West Brom continued their recent record of bringing about a Premier League manager's demise when their 3-0 win over Sunderland resulted in Paolo Di Canio being sacked last weekend.
Roberto Di Matteo, Mick McCarthy, Andre Villas-Boas and now Di Canio have all departed after league defeats against the Baggies in the last 18 months.
With approaching 20 years in the job and his side top of the Premier League, there'll be no such insecurity for Arsene Wenger at The Hawthorns.
The Gunners' recent record against the Baggies - winning the last four meetings - will give the Frenchman even more cause for optimism.
Steve Clarke has insisted his Albion side won't have one eye on Saturday's trip to Manchester United - a wise move considering Arsenal have won their last 10 games on their travels.
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 Capital One 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.
