Newcastle United exited at the second round stage following a penalty shootout defeat to fellow Premier League side Burnley.
The Magpies controlled the majority of the game, with Dwight Gayle and Jeff Hendrick on the end of their gapping chances.
However, a breakthrough could not be found and Sean Dyche’s Clarets advanced on spot-kicks after Allan Saint-Maximin and Miguel Almiron were denied by Wayne Hennessey.
“We played very well on the night, I have to say,” Bruce insisted.
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“I can’t really remember my goalkeeper having to make a save.
“We’ve created some great chances and we didn’t take them.
“Unfortunately for us, it proved costly but I couldn't fault the way we played.
“There were a lot of very good performances out there.”
Bruce said in the build-up to the game he wanted to take the competition seriously.
His nine changes – Jamaal Lascelles and Freddie Woodman the only players to remain in the starting XI – almost paid off.
Ultimately though, United’s long wait for a trophy continues.
Bruce added: “I’ve said since I walked through the door that I know how important it is and it’s an opportunity.
“I’ve said many times it’s going to be difficult for us to win the Premier League but a cup competition as a Premier League team - there are already two out, so a Premier League team can have a chance of a cup run.
“We got to the quarter-finals last year and the year before, so I’m disappointed we haven’t gone through.”