The pair were forced off during Villa's 1-0 victory over Tottenham at White Hart Lane - a Premier League encounter settled by Christian Benteke's first-half header as Tim Sherwood enjoyed a winning return to his former club.
However, injuries in either half to Clarke and Agbonlahor look set to rule them out of next weekend's trip to Wembley, while Carlos Sanchez's red card sees him miss out with suspension.
Asked whether Clarke and Agbonlahor are struggling to feature, Sherwood told reporters: "It looks like it, which is a real shame because it's a massive day out.
"Ciaran Clark came off with a medial knee ligament problem but I thought [Nathan] Baker did brilliantly when he came on, considering he's not played much. Gabby has tweaked his hamstring."
Two second-half yellow cards saw Sanchez earn a late red card, the latter of which came about after a foul on Danny Rose when Spurs were pressing for an equaliser.
"At first I thought he was being clever, with Man City away coming up, but someone reminded him it's the semi-final [he misses]," Sherwood joked.
"He's sacrificed himself for the side, he's probably never played at Wembley and he's going to miss a semi-final.
"He did it for the cause and we have to applaud that - their momentum was forward, he had to make the tackle. We're sorry for Carlos but we're very grateful.
"If we hadn't won [at Spurs] I wouldn't have enjoyed it but I show a lot of respect to the FA Cup, it's the greatest competition there is apart from the Premier League.
"We were never going to chuck it but we can concentrate on that one million per cent."
