Toon were eliminated from the competition on Wednesday after Kasper Schmeichel denied two spot-kicks, one of which from Shelvey, in a penalty shootout after the game finished 1-1 in normal time.
After the game Shelvey told the Evening Chronicle: "I want to apologise to the fans for missing the penalty. It was a shocking penalty on my behalf. I won't be taking them any more.
"I just wanted to come out and apologise to the fans.
"I thought we deserved more from the game and we worked our socks off against a very good Leicester side."