Sheedy played his part in the victory in Llanelli before being replaced in the second half by Jarrod Evans, who has returned to Cardiff from Harlequins this season.
With Ioan Lloyd, who is currently injured, also in the Cardiff ranks, head coach Corniel van Zyl has three Wales fly-halves to call on.
“All I can do as a player is try my best and perform the best I can,” said Sheedy.
“We all want to be number one, so how we go about that is going to be challenging because we’re all going to want to play.
“I’m sure it’ll be healthy competition.”
Cardiff return to the Arms Park to face Zebre on Friday night, where they lost only one home game last season.
“It does make a big difference,” said Sheedy.
“Hopefully we get a big crowd because I remember last season there were a lot of close games, and in the last 10 minutes, the crowd got us over the line.
“Corniel speaks a lot about making the Arms Park a fortress and we managed that last season.”