Cork and his teammates had to stand up to something of an onslaught from their opponents in the first half-hour at the Liberty Stadium.
The visitors eventually found their feet and were good value for their draw, leaving the midfielder satisfied with his afternoon in south Wales.
"If we'd have played this game at the start of the season, we might not have weathered that storm," admitted Cork after making his 100th Southampton appearance.
"We might have conceded and lost the game, so it shows how far we've come this season that we've picked up a point at such a crucial time.
"A lot of teams struggle to deal with the way Swansea play here, so it was a good point for us in the end.
"In the first 15 minutes we didn't really know what hit us at times," he continued. "They had some good spells so we had to really concentrate defensively.
"We tried to think of a harder game we've had all season – maybe Everton or Liverpool away.
"It's really hard when you're without the ball because they play little passes through the lines and pick up little spaces, and it took us a while to get used to it.
"Everyone knows how good they are passing-wise and technically, so it was a tough game and a good point for us in the end."
Today's result means Saints are now unbeaten in their last six games and Cork says they will look to push on during the remaining month of the season.
And the 23-year-old says that push for the top half of the table will start with a revenge mission against West Bromwich Albion, who beat Saints convincingly last November to leave us bottom of the league.
"It's a good way for us to be going at this stage of the season. We've got West Brom at home next week, and we'll always fancy ourselves there.
"We owe them a bit for how it went at their place, so it'll be a good one to get three points in.
"That was the week before I came in [after injury], but I remember how down everyone was after that.
"They've done brilliantly to pick themselves up and go on the way we have – we're in a completely different place and a different mentality to how we were then."