The Cottagers will play in the Premier League for the first time since the 2013/14 season after Cairney’s strike secured a 1-0 win over Aston Villa in the Championship play-off final in May.
And Cairney finally put to rest any speculation surrounding his future at the club by signing a new five-year deal.
They won promotion to England’s top flight after going on a good run during the second half of last season.
At the centre of the charge was teenage sensation Sessegnon, who has scored 16 goals as well as providing eight assists for Fulham so far.
The 18-year-old has been linked with a move to some of the Premier League’s top clubs this summer, while Ryan Fredericks made the move across London to West Ham.
But Cairney is hoping the Cottagers’ dressing room doesn’t get broken up too much.
Speaking to talkSPORT’s Jim White on Bob Mills, Cairney said: “I’m hoping he [Sessegnon] stays and I’m hoping a lot more of our players stay.
“I think it’s important to keep the squad together in the dressing room that got promoted to the Premier League.”
On signing a new deal as well as Fulham’s chances for next season, Cairney added: “I’m delighted to get the deal done.
“Last season was a bit of a crazy season. We went on that run and we finished it with what was probably the best day of my career at Wembley.
“We need to bring in other players because everyone knows just how hard it is to stay in this league.”
“I know I’m biased but in my opinion we played the best football over the last two seasons. We played Premier League football in the Championship which is not easy to do.
“I hope that we turn a few heads and do ourselves justice in the way that we play. Results are the most important thing but I really want us to stick to our philosophy and take a few teams on.