Cortese publicly put pressure on the Saints boss this morning on Radio Solent by stating he is not satisfied with the team's results in League One.
After Saturday's 1-1 draw at Exeter, Saints are now 15 points short of the playoffs, which Cortese described as the "top priority", with just 18 games left in their season.
In a statement issued through a local radio station, the St Mary's chief said that, although a trip to Wembley would be great, that is not what he is most concerned about.
Cortese said owner Markus Liebherr had made a significant investment - with nearly £2m thought to have been spent on players in January alone - and the reason for that was so Saints would make the playoffs.
Cortese added that recent league results have "not been satisfactory against that objective".
When asked for his response Pardew was fairly muted.
“They’re his opinion and I can’t change that,” he said.
“If he feels they’re fair then they’re fair.
“We’re just trying to have a really successful season the best way we can,” he added.
When asked whether the timing was appropriate he commented: “I’m not questioning anything.
“It’s his prerogative.
“I’m just the manager of the football team and I’m trying to do the best job I can.
“There’s always pressure on a manager.”
Saints currently face a massive week, with tomorrow's Johnstone's Paint Trophy area final second leg against MK Dons, followed by Saturdays FA Cup fifth round clash at home to Pompey.
Their next league match is away to leaders Norwich on Saturday, February 20.
And Cortese heaped extra pressure on Pardew ahead of that fixture, by stating he is "looking forward to the team getting back to winning ways" at Carrow Road.