The Toffees slipped to 12th in the Premier League standings with a 3-2 home defeat to West Ham on Saturday, leaving Martinez's men 12 points off the Champions League qualification places with 10 matches left.
Everton finished fifth in Martinez's first season in charge, but have failed to match expectations this term despite the financial boost provided by new majority shareholder Farhad Moshiri.
"I think Martinez in his interviews is becoming a joke and an embarrassment," Sutton said on BBC Radio.
"After every game he blames everybody, everybody other than himself. Whatever you say about Mirallas at the weekend, he deserved to go off. What is the argument?
"He blames everybody, but ultimately he has sort his team out defensively.
"Have they underachieved this year? Absolutely."