The Premier League champions were made to sweat by the resilient promoted side before the England man headed home in stoppage time.
"I am relieved and delighted at the same time to get a goal that late," Barry told reporters. "You are starting, probably, to panic, thinking we are going to drop some big points at home again.
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"They started to believe they could keep us out for the 90 minutes - even towards the end they were believing they could maybe get the winning goal."
Though Royals boss Brian McDermott argued that the goal should not have stood, Barry recalled: "At the time I felt I just got up and Nicky Shorey was just standing there.
"I probably went over the top of him. I'm delighted the referee hasn't seen it as a foul."
Late goals were instrumental in City's title triumph last season and the midfielder encouraged his team to continue pushing throughout matches.
"You have got to [keep going] at this level," he observed to the club's official website. "We scored so many late goals last season and a few this year.
"Those late goals can be so important at the end of the season and hopefully that will be another one."