Chris Wilder's side made it three wins in a row and stretched their unbeaten run to 10 games thanks to a narrow victory sealed by Peter Leven's 16th-minute spot-kick.
Referee Fred Graham awarded the penalty after Tom Craddock had his heels clipped by Sido Jombati as he raced into the box.
Yet Yates said: "The ref never gave any free-kicks all game and then gave them a penalty that never was. I've seen the game back and it was never a foul.
"It gave Oxford something to hang on to and they were able to play on the break in the second half.
"I thought we were the better team. It was a stupid goal that we gifted them.
"I thought we had a few chances in the second half but our finishing was a bit disappointing."
Yates added: "It was a toughly contested game on a difficult, tacky pitch with no real quality on view from either side.
"I was pleased with the attitude of my team. We were more committed and more professional than we were against Rochdale (in a 4-1 defeat).
"We did okay but neither team played with much fluency. We've lost, we've got to move on quickly."