The 26-year-old midfielder turned down what was believed to be the most lucrative contract in The Railwaymen's history to stay in the championship and sign for Paul Sturrock's men.
His signing is a massive coup for Sturrock after he fought off competition from Wolves, Leicester and Stoke for the playmaker.
Gradi tried his hardest to keep him at Gresty Road but in the end a move to Hillsborough seemed too good to turn down for the Runcorn-born Lunt.
The Crewe manager told the Sentinel: "We made Kenny a very good offer, but the offer he received from them was more than double what we made. It blew ours out of the water.
"With Kenny, he has not just gone for the money. He weighed up the football and I think if we had stayed up he would have thought twice about it. It was the first concrete offer he had, and he felt it was now or never for him. From a footballing point of view, I understand his reasons for going.
"I wouldn't expect him to go there as captain, but he will go there with opinions and I would expect him to be playing a lot of football."
But veteran Gradi, who has seen most of his top players leave over the years, including Owls new boy Madjid Bougherra, still hopes Lunt will a massive part of Crewe's future.
He added: "We are hoping he will be able to stay and help us with the young players at the academy on Sundays so we are not severing all ties with him."