Adams has been concerned with the balance of his side lately and believes his team was too open in recent matches.
But he stuck to his guns with Peter Crouch in the lone striker's role and was happy to go to Ashton Gate on Tuesday week for a replay.
Adams said: 'I thought we could have won that on the chances that we created, but it was important to keep a clean sheet.
'Bristol City are a difficult team to break down. They are very organised and very resilient and we didn't quite manage it.
'We're still in the hat, it's a good clean sheet and it's something to build on.
'Sylvain Distin had a good chance with a header and Niko Kranjcar had a couple of opportunities.
'On another day we would have won the game, but it was important to stay in the FA Cup.
'Niko and David Nugent were getting up there alongside Peter Crouch so it was a three up there and not just one. But we didn't want to commit suicide like we've been doing at home recently.
'There is a balance in football and we got the defensive side of the game right.'
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