The Hoops were crowned Scottish champions for a 44th time after defeating Butcher's Caley side 4-1 at Parkhead.
Former Rangers defender Butcher said: "Celtic are worthy winners. They are difficult to stop when they are in that mood, especially when there is a title at stake.
"It is difficult for Celtic because they have not had Rangers with them.
"When I was at Rangers I couldn't have contemplated not having Celtic there pushing you. But Celtic have got there and got a cup final to look forward to.
"They are a good team and when they are enjoying their celebrations, we will be having fish and chips."