It was the first time the leaders had failed to score in a Championship game this season.
Adkins said: "We didn't test their goalkeeper enough. We may have lost to two deflections, but you have to give Bristol City a lot of credit. They are on a good run at the moment and the ground was really buzzing.
"As always, I shall analyse our performance very carefully by studying the match DVD. I hate losing and so do the players so we won't be taking the result lightly.
"It's important we bounce back quickly in our next game against Hull. We probably had the best week's training since I joined the club so I was confident of a good display.
"Bristol City proved very difficult to break down and we have to assess whether that was a result of their good play or our deficiencies."