In his first game in charge, Cotterill admitted there was plenty for his troops to work on.
"The players have had a tough week this week - with a new manager coming in, they don't know what to expect, not quite sure what to do, what to say, how to play," he said.
"Because of the DVDs I've looked at, I probably knew more about Tamworth than my own team!
"So we had to make sure we came through this and I thought the players showed very good character. Tamworth had some big boys, they were a bigger team than us and we had to stand up to that."
By contrast Tamworth boss Dale Belford was left to rue what might have been after the non-league outfit missed out on an upset.
"Obviously we are disappointed with the end result, but the amount of effort and commitment the lads have shown is a credit to this football club," he said.
"We've just fell slightly short against a, let's be honest about it, really good side. They were in the Championship last year.
"And I just felt we couldn't give any more. We were a little bit unlucky with the chances we missed."