An injury-time winner from substitute Farid El Alagui saw Brentford progress into the second round at the Daggers'expense, but Burnett was pleased with his team's performance.
He told London24.com: "We knew it was going to be a tough game coming here but I am proud of my players.
"I'm really disappointed with the result but I am proud of my players because they worked incredibly hard and didn't look out of place against a good League One team.
"I think we deserved the equaliser. We tried to put pressure on them.
"In a cup tie you are 2-1 down, you might as well lose three or four if you are going to get beat because you are going to be out anyway.
"Josh (Scott) had a chance at 1-0 and he's hit the crossbar and that might have made it a different game but that's football I guess."