Celtic, who clinched the title with a 4-1 win over Butcher's side at Parkhead, went into the game only needing a point but did not come to life until after a dull, goalless first-half when goals from Gary Hooper, to take his season tally to 28, and a strike by stand-in skipper Joe Ledley in between, got the celebrations fully under way.
Georgios Samaras, on for Anthony Stokes, completed the scoring with a virtuoso goal two minutes from time before Caley's Aaron Doran got a late consolation for the visitors.
Butcher, a former Rangers defender, 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."