Stephens marked his 24th birthday with his first goal for Southampton.
“It was perfect day for me and great of course to get on the scoresheet but the most important thing is the result for the team and for the club," he said.
“We wanted to progress in this competition and we got the result that we needed. We've had the experience from the League Cup last year; if we could replicate that this time around in the FA Cup, it would be unbelievable."
After conceding twice in the second half at Vicarage Road in the Premier League, the Saints defence withstood a late barrage from the Hornets this time around to earn a “pleasing" clean sheet.
“It was a similar game to the one at their place a couple of weeks ago; we played very well in the first half, they reacted by going more direct and we were ready for it.
“We dealed with the high balls a lot better today so it's a really pleasing clean sheet for us. We haven't earned many of late so to get one here and win was important."