Saints secured their first win since the former Espanyol boss controversially replaced Nigel Adkins at the helm, beating Manchester City 3-1 at St Mary’s.
The reigning Premier League champions were well and truly outplayed by Saints, who hassled and harried their way to victory.
Much has been made of the pressing game employed by Pochettino since his arrival - a system midfielder Cork is enjoying.
“It does feel like you need two hearts to play like that," he said.
“It is hard work but you can see the result and hopefully if we can keep that standard going, we can hopefully do that every week.”
Saints have only lost three of their last 16 Premier League games now, after suffering eight losses in their first 10 games back in the top flight.
“We've been playing well for quite a while now - it is a good two or three months we've been picking up a few results,” admitted Cork.
“The last few games under the new gaffer we've been playing some really good stuff.
“After a great game like that against City, there is no reason why we can't keep going and get higher up the table.”
Saints moved six points clear of the drop zone with Saturday’s win, which Cork compared to the high of achieving automatic promotion from the Championship last year.
“I’ve had some great times at this stadium,” he said. “When we went up last season, the fans were unbelievable then.
“That was up with that day. “When the final whistle went and you see the fans go nuts and to see the lads so happy, it was a great three points.
“It takes us six points clear and it is almost as big as when we went up last year. Hopefully we can keep that gap at six points and push on.”