Ally McCoist's side have dumped Motherwell from the Scottish Communities League Cup, and Hutton is keen to take another top-flight scalp against Inverness tonight.
He said: "We just want to prove we are still good enough to compete at that level, the level we want to get back to.
"We need to go out and show everyone else that is the case.
"I think we would do fine [in the SPL]. In the Third Division, we are still trying to get used to it a wee bit but on Sunday, we got our first win away from home at Clyde. We are trying to get used to it.
"We are more comfortable playing the Premier League teams.
"I think we would be fine competing in the Premier League with this current squad.
"We know what to expect after the last game with Motherwell.
"We played really well at Ibrox and don't fear anyone there.
"We just need to go out and do the business and, hopefully, get the victory."