The 21-year-old curled in the winning goal during first half stoppage time after fellow Reds prospect Jack Dunn had levelled for Paul Buckle's Robins in the 40th minute.
"It doesn’t get any better than that really and I owed the goal after losing it in the build-up to their goal, so I was really happy to get the goal for the team," Stewart said.
"It went though a lot of bodies, so the goalkeeper didn’t see it until late. We came here to win and get the team up the table so we want to go on a run now."
Stewart spent time on loan at League One side Crewe Alexandra two seasons ago, during his time at Tottenham Hotspur, but he said League Two presented an altogether different challenge.
"I found it very different to when I was at Crewe because it was a lot more physical, with a higher tempo and you don't get any time on the ball," he said. "It was a new experience for me, but I am looking forward to the next one now.
"The main thing is to get games and build experience, so I was very happy to play 90 minutes on my debut."
Stewart started in a deep lying midfield role at the Kassam Stadium, having recently made the switch from left-back in the middle of the pitch under Liverpool's academy director Alex Inglethorpe, with whom he also worked at Spurs.
"That was only my fourth game in the middle, but I prefer it there," he said. "I was deep at first against Oxford, then went I higher and it’s about adapting to what the gaffer wants me to do.
"Alex Inglethorpe told me to make sure I show my strengths and adapt to whatever is asked of me.
"I don't score many goals and I don't think I have scored a winner since I was a little kid, so I was very pleased with that!"