The defeat leaves Rovers with just one win from their last nine league matches, and Barnes said: "That was not a good game for us, especially in the first half. Millwall are a good side but we made them look like the best side in the division in that first half.
"Ultimately there are two disciplines in football, what you do with the ball and what you do without it. We were wasteful in both and you can't excuse that.
"They're all trying physically, it's just the concentration that's let us down. When you don't try you can't accept that, but they are trying so I can't fault them for that.
"You always fear for your job, but whatever happens happens, all I can do is do my best to get the best out of the players."