Kone was tracked by Allardyce when the Sunderland boss was at West Ham.
Kone said the facilities at the club meant everything is geared towards the side operating in the top flight and admitted the club is bigger than he thought it would be.
He is quoted in the Chronicle, saying: “Everything is sort of geared to be a Premier League club. It’s bigger than I thought it was, and bigger than Lorient, although the situation was a bit better at Lorient, more mid-table.
“It’s vital to stay in the Premier League. My goal since I’ve come here is to win as many games as possible and keep the club in the league."
Kone was also tracked by Sam Allardyce when the Sunderland manager was in charge of West Ham United last season but a deal couldn't be agreed.
However, the defender was made an offer that he described as 'attractive' to head to the Stadium of Light as he was sent something of an SOS by Allardyce to help fight the relegation battle the club are currently in.
Kone added: “How did Sam Allardyce sell the club? He just said he wanted me to come and help the club stay in the Premier League.
“Sunderland made an attractive offer for me. There were other clubs interested but none of their interest came to anything concerete.
“I found this an interesting project because of the idea of helping them in the relegation battle. I spoke to Sam Allardyce, who said he needed me in a relegation battle, so that appealed to me."
They are currently four points adrift at the bottom, but the £5 million signing from the Lorient has shown signs that he could be a valuable addition between now and the end of the season.
Kone impressed on his debut against Manchester City, and received praise from his manager during the side's 2-2 draw with Liverpool at Anfield.