Shelvey opened the scoring on the 61st minute with a deflected 25-yard strike, with a goal from Chico Flores sealing the victory which lifted Swansea up to 10th in the Premier League table.
The former Liverpool man understood the importance of the game, and expects the result to provide a huge lift for the team.
He told the club's official website: "It was a massive win for us. I felt we needed it to get us back up the table and away from the danger zone, because it is very tight down there.
"I can understand why the fans are a little nervous, but it's down to us to get us out of this. We are trying to stay calm and play without pressure even though we are in a sticky situation.
"We stepped up a gear in the second half, though. The gaffer said at half-time that we needed to up the tempo, get the ball wide and get the crosses in - that's what we did."
Shelvey has enjoyed more regular football at the Liberty Stadium, and has scored four goals in 26 games for the club this season.
The 21-year-old added: "I had a few shots - I should have scored the first one that was put back to me in the first half - and then I hit the crossbar, but luckily in the second half my goal took a deflection and went in. It was on target anyway, so I'm claiming it.
"And the second goal really took the pressure off straight away - I'm glad Chico got it.
"So it was a good night for us. This win eases the pressure a little bit, but February is a very busy month for us so it's important we win our home games."