The south-coast club's return to the top flight did not get off to the best of starts, with just one win to their name after 10 games.
They conceded 28 goals in that period but have since shored up at the back and have suffered one defeat in their last six matches, conceding just four goals in the process.
That turnaround has coincided with Cork's return from injury but the midfielder was keen to avoid any praise, instead highlighting a change in approach as the reason for the improvement.
"When you're going through a bad patch, the thing you do is look at everything you are doing wrong and try and put it right," Cork said.
"The manager came in and said 'what do you lot think we're doing wrong?' Everybody put their own input in, we changed things we needed to change and it worked for us.
"A couple of months ago we had a few talks and we had a few things around the training ground and stuff.
"We all decided as a team what we needed to do to put things right.
"We focused on different things at the training ground, a lot more people spoke up.
"We created little groups and stuff at the training ground to talk about certain issues.
"I think just everything has come together at the right time when things when were looking bad and somehow we all just pulled together and started picking up a few results in big games we had."
Such performances saw Saints secure victories against sides around them and Cork believes a new-found defensive resilience has been key to that revival.
"The team just seems a lot more defensively assured," he said.
"We have not conceded as many goals as were at the start of the season.
"We just look a lot more confident in our defensive play and obviously with the attacking players we've got we always know we're going to score.
"As long as we stopped conceding goals, we always knew we would start picking up points because the attackers always do their jobs for that."
Saints will be looking to continue their impressive form when another struggling side come to St Mary's on Saturday.
Sunderland have lost three of their four matches this month, including last weekend's 3-1 defeat at Manchester United.
Saints, by contrast, have had a two-week break due to their scheduled fixtures against Chelsea being postponed due to the west Londoners' World Club Cup commitments.
"It has given us a little bit of time to recharge our batteries and getting going again for this busy month," Cork said.
"If you look at it another way, it gets you out of the flow of the games.
"We were on a half-decent run and maybe having that game last weekend would have kept the game going.
"We'll have to see and hopefully the game has done as good and go into the next game with the same sort of confidence."