A double from Malta international Daniel Bogdanovic booked the Tykes' place in the third round and eased the pressure on under-fire boss Simon Davey.
And Gray, who completed a permanent move to Oakwell this week, feels the Reading win will spur his side on to better things.
"It was our first win for a while on Tuesday and it has been a big weight off our shoulders," he told the club's official website.
"You can see that everybody is a lot happier around the place and there has been a real spring in the players' step in training.
"Hopefully it will be first of many."