Piero Mingoia's brilliant long-range equaliser in stoppage time was added to by Luke Berry's 118th-minute winner.
"There were some really mighty performances by everybody connected with the club," Derry said.
"As the game developed, and especially into extra time, I felt we deserved it and looked like the strongest side."
It was the first time the U's had won a League Cup tie in 14 years - the last victory coming against Reading in September 2002.
"I'd have been proud to take it to penalties and proud of my team regardless of how it would have ended after penalties," Derry added to BBC Radio Cambridgeshire.
"But to get the winning goal with a couple of minutes to spare that just tells everybody what we're about.
"We've got a desire and a togetherness that makes a manager very proud."
Cambridge United boss Shaun Derry has hailed his side after their extra-time win over Championship club Sheffield Wednesday in the EFL Cup.