The former Chelsea and Brighton manager mastermined Sweden's unlikely late push to qualify for the summer's tournament.
Victory over Poland came in the 88th minute as Arsenal striker Viktor Gyokeres struck to earn the 3-2 win.
Potter remarked afterwards: "(I felt) like I had some kind of out-of-body experience, to be honest - I look at the goal and then most of the people from our bench run out onto the field, and I'm like, 'Am I here?' It's just one of those moments that I'll be forever grateful for.
"Incredible night. Wow, just to be a part of it is an incredible honor and an incredible experience. I'm just so happy for the team. It was tough, but I'm just incredibly proud of the team. It was a dramatic match, so hard to control, the emotions and what's at stake."
Potter admitted that it was a wounded team when he came in as manager and explained how he managed to pick them up.
He stated, "It was just about trying to get the team together. There's talent in the team, but talent as an individual is not enough, especially at international level.
"We had to try to get the team together and create that as a foundation and obviously we have players who can cause problems and we're trying to do that. I think at the end of the day it's about the team and how we collectively fought for each other out there. I was proud of the team."