The Robins came flying out of the blocks, and dominated the opening 10 minutes of play.
But after restricting the visitors, United came back into the game and were deserved winners.
"After the first 10 minutes we started winning the ball in the middle of the
park, and that was all down to Hinds and Goodwin.
"We weathered the storm, stuck in there, and I thought they did brilliantly.
"We started winning the knockdowns in the middle of the park, Goodwin and Hinds were responsible for that, and that gave us a foothold in the game."
Adkins also praised the work-rate of his team, who constantly chased seemingly lost balls and forced the visitors into several errors.
And with his side now three points clear at the top of the table - five ahead of third-place - Adkins insists there is nothing to stop his side gaining a remarkable promotion to the Championship.
"Bristol City are a top team, we new we had to deal with them from set-pieces and to get the ball back from then when they were on it," added Adkins.
"I'm delighted, all the players were totally committed to the cause. They've gone out and worked hard on a cold frosty night, playing on a pitch not suitable for football but got on with it and trying to play
"There is a belief among the players, that's been there right from the start of pre-season when we went to Ibiza. The players work really hard for each other to create opportunites - and Billy Sharp's goal on his birthday was the icing on the cake.
"A couple of years ago we nearly went to the Conference but the next season we got promoted and got belief from that, now we're givining the supporters the chance to dream of the championship.
"We are chasing the dream and have to keep believing in ourselves and see what happens. We've got good players, if we keep working for each other we've got a chance"