The match official awarded a penalty to the Potters which was converted by Marko Arnautovic in injury time to give the visitors a last-gasp 4-3 win at Goodison Park.
Martinez believes Clattenburg got it awfully wrong as Toffees defender John Stones made contact with the ball when sliding in on Arnautovic and felt aggrieved his side did not come away with at least a point in what was a quality contest on Merseyside.
"The feeling is extra frustrating today because you cannot understand how such an experienced referee gives that decision right at the end," said the Spaniard.
"It is such a wrong call. Someone with his experience should understand the game a bit more.
"Clearly John Stones gets a touch of the ball and from that point on you can see there is a doubt from the referee.
"He does not give it straight away, so he wants confirmation, and he waits for the linesman - who is probably about 45 yards away from the incident - to give him his view.
"It is very disappointing at that point for us to lose a draw."
Martinez added: "It is a game we didn't deserve to lose and it is one where we should have got a lot more," said Martinez.
"Obviously we want to win these sort of games, but if you can't win it we should never have lost because of that terrible decision from the referee right at the end.
"The disappointment is that he got that one wrong, but it is extra painful when he wasn't consistent throughout the game.
"To give a penalty in the 90th minute, you have to be certain, and you use your experience on that. When you are not certain, it is very strange to see an experienced referee doing that."
However, a fine strike from substitute Joselu drew Stoke level on 80 minutes before the dramatic winner from Arnautovic broke the hearts of the home side.