On Saturday 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.
Much has been made of the pressing game employed by Pochettino since his arrival, and Cork said: "It does feel like you need two hearts to play like that. 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."
He went on: "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.
"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."
Southampton 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."
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