The on-loan Brighton goalkeeper was named in the Championship Team of the Season and also nominated for the Player of the Season award at Sunday's EFL Awards.
King told talkSPORT: "We had Oliver Dovin last year and Ollie was going great and had a really unlucky incident at Sheffield United.
"We recognised we needed a top goalkeeper, therefore, for this season.
"We knew Carl had had some tougher times. He went to Hull, got injured, got pulled back to Brighton.
"We obviously follow a lot of people, we always thought he was a very good goalkeeper. We did try and buy him, that’s documented, in the summer. That got short-changed from Brighton.
"But they were really happy to showcase him with us at, hopefully, the top end of the Championship and obviously he’s had a great season.
"I haven’t even thought about it (signing Rushworth permanently). He’s a loan player, he’s Brighton’s player. He’ll go back on June 30th and then we’ll see how it all stacks up on a lot of things."