It needed 22 penalties to separate the two sides before Blades goalkeeper Steve Simonsen missed the decisive spot kick, while Clarke capped an impressive all-round display to coolly dispatch his penalty at Wembley.
Clarke said: "To be honest with you I wasn't too nervous. It was just a little bit surreal at times, but thankfully we were on the right side of it.
"Sometimes these things go your way, sometimes they go against you. You've got to feel for Sheffield United, but we tasted defeat in the final last year. Maybe it was just our turn."
The former Everton, Blackpool and Southend centre-half turned in a real captain's performance, twice going closest to breaking the deadlock with second-half headers while proving a colossus at the back with several last-ditch tackles.
Clarke added: "Maybe so. It was a good afternoon and good for me personally, but that wouldn't have mattered one little bit if we hadn't won the tie."