Saints' 3-0 reverse at Everton on Monday completed a difficult Christmas period for Claude Puel's side.
But Stephens, who made his Premier League debut at Goodison Park, believes a change of form is on the cards.
"We just need that little bit of extra luck, or extra quality to go 1-0 up," he told BBC Radio Solent. "These things happen and we'll bounce back."
Stephens, 22, found himself introduced in the sixth minute at Everton, when injury forced Cedric Soares off.
"I enjoyed playing the game," he said. "But at the end of the day, I want to win and being on the end of a 3-0 defeat isn't good.
"We'll pick ourselves up and work hard and I'm sure it will turn round. I don't think there's too much wrong, it's not a disaster and it's not time to panic."
Southampton defender Jack Stephens has insisted it is "not the time to panic" despite their third defeat in six days.