The Blues, impressive against Cardiff City in the 53-year-old's first game in charge last week, succumbed to a 2-0 defeat in South London through a couple of second-half goals.
Despite Birmingham coming unstuck in the second 45 minutes, Cotterill believes that his side's struggles started well before then in what he describes as a "tentative" performance.
"All in all the work we have done I wouldn't do any different if we played them again next week. We just didn't get a proper foothold in the game," he told reporters. "I thought we were just a bit tentative in everything we did in the first half and if you are like that here - a hostile environment, the way they play they can hurt you with that.
"The first thing we needed to do was stand up to that long ball, diagonal, straight, aerial bombardment, backing it up, seconds balls and we never won enough of those. You have to go through that fight to have the right to play. It's disappointing, we prepared all week, there has not been any surprises out there on the pitch today.
"I know the goals have come in the second half but I think we laid the foundations for getting beaten with our first half performance when we were more disappointing. I know we have conceded the goals but we were actually better in the second half, our passing was better, we were crisper with it, we won a lot of the first contacts, the first headers and a lot of the second balls - whereas we didn't do any of that in the first half.
"The players in there are disappointed themselves. I didn't expect that at all, I thought we would be far better at dealing with Millwall's threats. I said at half time if we carry on in the same vein 100 per cent we will get beaten today because one of us will make a mistake and they will score a goal."
Birmingham have just three wins to their name this season and are currently one point above the relegation zone.