Stewart's late penalty saw Saints win this fifth round FA Cup tie 1-0 at Craven Cottage.
He later said, "Amazing feeling. We put so much into the game, had a massive support here today and to get the win in that manner is really cool. We can look forward to the draw now.
"We came together after January with the squad we've got and we've put in some great performances. We've got a lot of confidence and we were a match for a team in the league above us.
"We missed a few (chances) but we were creating. We kept plugging away and we were solid at the back which gave us a platform. When you keep clean sheets you only have to score one and we did that and timed it well that we didn't have to see it out for too long."
On suffering ACL injury at Craven Cottage while playing for Sunderland, Stewart also recalled: "Not the fondest of memories from that day. Good to come back and freshen up the memories with some good ones. Don't want to think too much about that so it's good to move on."
On his penalty, he added: "I love those moments, back myself and practice them a lot. Great to see it hit the net.
"Whoever we get is a tough tie, a lot of teams will probably fancy us. A home tie would be good but they'll all be tough."