He told the club's website: "It felt really good. Not so long ago I thought that I wouldn't ever really play [in the first team] because my contract is up in the summer.
"So just to get the chance to play was great, even if that's my one and only appearance then it's been such a great experience.
"I've been thinking about what I'm doing to do when I leave here, but hopefully now I could stay, or at least I've had the chance to put myself in the shop window."
Williamson only found out he was in the first-team squad when coach Derek Fazackerley told him on Friday.
"We'd been out training, and I'd been training with the first team, but I wasn't expecting to be involved. Afterwards, Derek Fazackerley came up to me when I was having my lunch and just told me I was in.
"So it was a bit of shock and I thought: 'Right, change my plans for the weekend then!' I thought he was joking at first."