The Brewers took the Premier League side all the way to penalties at the Pirelli Stadium on Tuesday night.
The Cottagers finally prevailed 5-4 on spot kicks after a 2-2 draw following extra time.
Martin Jol's men looked comfortable with the first-half lead given to them by Adel Taarabt but Jack Dyer, who saw his penalty saved by David Stockdale in the shoot-out, equalised after 85 minutes to send the tie into extra time.
Rowett said: "I thought we had some brilliant performances.
"To almost knock them out was incredible. I thought we were brilliant, absolutely brilliant.
"We've got a brilliant group of players here and over 90 minutes we are still technically unbeaten this season."