Southampton's 3-1 victory over champions Manchester City on Saturday was their best result of the season, and Cork was arguably man-of-the-match for his all-action display in central midfield.
Pochettino's appointment, after the hugely controversial dismissal of Nigel Adkins, was a major surprise but Saints have been much harder to beat since his arrival.
"It does feel like you need two hearts to play like that," Cork 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.
"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 are four points clear of the drop zone after 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.
"The victory over City 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."
Given such impressive form there have been suggestions Cork, part of the Great Britain squad at London 2012, could win an England call-up.
"I don't know, really," he said, when quizzed on the issue. "I wouldn't want to say anything about that. I just want to keep doing well for Southampton.
"We had a bit of a tough start and as long as we can stay in this league and I can put in as good a performance as I can each week that is all I am really wanting to do at the moment."