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.
The reigning Premier League champions were well and truly outplayed by Southampton, 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.
"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.
"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."
Cork was arguably the man of the match against City and has impressed since returning from the injury problems that blighted his start to his season.
The 23-year-old only made his first league start in November and has since impressed fans and pundits alike, as well as team-mate Steven Davis.
"He was injured earlier on in the season but since he came back he made a real impact and showed a great level of consistency," the Northern Ireland captain said.
"Again against Man City he was one of the top performers and hopefully he can carry that form through to the end of the season."
Given such impressive form could Cork, part of the Great Britain squad at London 2012, foresee an England call-up?
"I don't know, really," he said. "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."
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