Davis, who will captain Northern Ireland in their friendly in Turkey on Friday night, has helped Saints in their unlikely rise to third in the Barclays Premier League table.
When he joined the club from Rangers last summer they were newcomers to the top flight but they have wasted no time in setting loftier aims than mere survival at that level.
Davis has praised Cortese for delivering on the promises he made when attempting to sign him and Pochettino for his bold tactical approach.
"It's still early doors this season, but you can see we're ambitious and you can see how the manager sets us up to be brave and attack," he said. "We try to dominate possession.
"A lot stems from the chairman as well. When I signed, what they portrayed to me in the talks has been backed up.
"It's been an unbelievable rise for Southampton from League One to where we are at this point in time but it's still just a start and there's a lot more room for progression."
Davis is also highlighting an element of personal improvement.
His maiden season at St Mary's included just two goals - though both were against the might of Manchester City - and he has already bettered that this term.
He netted twice in the Capital One Cup clash at Barnsley and again versus Hull in the final match before the international break.
The 28-year-old is targeting more of the same as the season progresses, but accepts breaking into a midfield including the reliable Morgan Schneiderlin and £12million Victor Wanyama - a former Old Firm rival of Davis' - is the first priority.
"It's always important for midfielders to get into the box and help out with assists and goals and I've managed to do that a bit this season," he said.
"I want to continue and get a good return. The way we play at Southampton and the position the manager has been playing me allows me to find pockets of space and get further up the pitch.
"But I picked up an injury at a bad time and it's hard to get back in. I probably have to bide my time now and wait for my chance to come round again because the team is playing so well."
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