Sutton believes Gordon Strachan has called it wrong after claiming his need to balance physicality with skill makes it difficult for Griffiths to lead the line for his country.
The national team boss has selected Derby's Chris Martin and Steven Fletcher of Sheffield Wednesday up top for the Scots' three World Cup qualifiers so far, leaving Celtic hitman Griffiths to be satisfied with two substitute run-outs.
Griffiths struck 40 goals for the Hoops last term yet that has not been enough to force his way into the national team starting line-up.
Now Strachan has tried to justify his decision to leave the 5ft 8in Parkhead frontman on the bench by claiming "you need to have a certain amount of height in international football teams to defend set plays".
"It's ludicrous," Sutton said. "Is Messi too small then? I just don't agree with what Gordon has said at all. It should be horses for courses.
"Scotland went to Slovakia and played a team with two centre-halves in Martin Skrtel and Jan Durica who love the physical side of the game but don't like being taken in behind. They left a striker on the bench who can do just that, so I think that Gordon is absolutely wrong with his point of view.
"He is wrong to play the likes of Chris Martin in front of Leigh Griffiths. If you want to win football matches you have to have people who can score goals."