The Scottish international scored the only goal of the game, completing a 36th minute breakaway to fire Rovers to a hardworking victory at the Madejski Stadium.
Conway has had to be patient following his arrival from Cardiff City at the end of January, but marked his first start in a Rovers shirt with his first goal.
"First and foremost, the three points was most important thing," said Conway afterwards.
"To score, from a personal point of view, was brilliant, and on my full debut.
"I think there was always going to be times that we had to sit in and catch them on the break and that is what happened. We got a few chances from that.
"Luckily the ball broke to me quite nicely and the boy slipped so I had a wee bit of time and luckily it went in."
Rovers had to withstand a spell of pressure in the second half as Reading pumped ball after ball into the penalty area, but Conway and co. stood strong to claim a huge win.
The midfielder added: "The second half felt like the longest half ever! With the nine minutes added on it was long and at parts we were probably hanging on there.
"But I don't think they had any real clear-cut chances, I think it was just pressure with balls coming into the box, but the two centre halves dealt with them so well.
"They had a good front two and in the end it was probably a front four but I felt we dealt with it really well.
"We hung in there and we got the three points that we came here for."
Conway and Rovers are back in action this Saturday when they travel to take on Bolton Wanderers at the Reebok.
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