Marcus Edwards' second-half goal secured the Clarets' place in the fifth round, marking their sixth consecutive clean sheet.
Shelvey, making his first start since joining Burnley in January, played 60 minutes as part of Scott Parker's rotated squad.
Speaking after the match, he said: "We limited them to a few chances. I felt we should have been two up in the first half, we had two great chances.
"But even when the other team is on the attack, I mean that was my first proper game. You just feel like they are never going to score.
"I can only speak for myself but the lads who have been here the whole season, I imagine that is what they feel like anyway.
"It is like a stonewall defence. We work on it daily but we also work on the attacking side as well," added the former England international.
"It is good to have that mixture. I Thought we were good this weekend in terms of that mix in keeping the ball and then going long as well.
"It was a good performance and the main thing is we are in the hat for the next round."