The Stadium of Light outfit brought the curtain down on their Premier League season on Sunday with a 3-1 home defeat to Swansea City, ending the Wearsiders' five-match unbeaten run.
But the campaign will be remembered for Poyet's heroics in lifting Sunderland from bottom of the league at Christmas to a 14th-place finish.
Despite survival, the Uruguayan's future at the club has come into question of late, but Poyet insisted manager-chairman meetings were natural at the end of a season.
"I want to inform everyone that every single manager in the world, when he finishes the season, has a meeting with the chairman of the football club," he stressed.
"Winning the league, going down, being in the middle, having a big name somewhere else, with contract, without contract - it's natural.
"Every now and then when a manager says 'I need to meet with the chairman to see where we are going', you all start to think 'oh, he's leaving', or he's not happy, or there is a problem.
"Now, I will have a meeting with the chairman, so I hope you understood what I said before.
"It's natural because I want to know where we are going, if it's possible not to make the mistakes we have made in the last couple of years, because I don't want to go through another year like this one, and because I like to plan."
When pressed on the issue, Poyet revealed he had already met with Short, but would return to the discussions after taking a break.
"I already had a meeting today," he added. "I don't know if the chairman is going to be happy I said that, but I saw him today and, I don't want to sound arrogant, but after my deserved break I'm going to come back and sit down again a little bit more fresh after resting."
However, Poyet later hinted he would remain with the club, adding: "Now my challenge is to give a lot next year."
Sunderland reportedly have seven players out of contract at the end of the season, including Sebastian Larsson, Phil Bardsley and Jack Colback, and Poyet revealed those involved would learn their fate soon.
"We're going to make an announcement to the players that we want to release," he said. "We didn't want to do that too early.
"And the ones that we want to have a few chats, it's going to be a negotiation. A player who finishes his contract and plays week in week, he can have a few options."
