Saints arguably deserved all three points after taking the lead through Gaston Ramirez in the 34th minute but were pegged back shortly before half-time when Guly do Prado could only direct Theo Walcott's free-kick into his own net.
Ramirez had the ball in the back of the net once more with an exquisite control and volley on the turn after the interval but it was chalked off for a foul in the build-up.
Midfielder Cork, who filled in at right-back today, was gutted Saints were held to a draw for their third consecutive game, but he was quick to hail the team's performance.
"It was a good point. I think we could have nicked it towards the end," Cork admitted.
"The goal was unfortunate that they scored but the lads put a real shift in today.
"We've had a real tough week, we had Stoke last game and the game before that everyone's worked really hard. It's been a busy Christmas period but we've got a few points."
Saints conceded a 3-1 lead to draw 3-3 at Stoke over the weekend but Schneiderlin echoed his team-mate's thoughts.
"We knew before the game that this was going to be very hard, we knew they were going to keep possession and that we needed to keep a good shape and we did at that at times," said the Frenchman.
"We were unlucky with the goal we conceded but we gave a good shift, we gave everything for each other."
For full match reaction don't miss tomorrow's Daily Echo.