The Premier League strugglers arrived at The Den with many predicting an upset, but goals from Ryo Miyaichi and David Ngog set the Trotters on their way to a comfortable victory.
"We knew when we came to Millwall that we'd face a good side in front of a cracking atmosphere," he said.
"The result was paramount today as we wanted to progress to the quarter-final, but the performance with it was very pleasing. We scored two terrific goals and could have had a couple of others, if truth be told.
"Millwall are always dangerous opponents, but the players stood up to them. We passed and moved the ball well and over the piece there's no doubt that we were worthy winners.
"We always looked as if we had goals in us and at the back we defended well and coped with periods of pressure."