Romelu Lukaku's 78th-minute header settled Wednesday's encounter at Goodison Park after Jesus Navas had cancelled out Ramiro Funes Mori's opening goal.
But Pellegrini believes Lukaku was offside when Funes Mori converted a rebound and was disappointed not to see Navas awarded a penalty having appeared to be hauled down by Kevin Mirallas in the box.
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"He's [Lukaku] absolutely offside," he told Sky Sports. "It's unbelievable the referee or the linesman didn't give that offside.
"It's [the Mirallas challenge] a foul inside the box, he doesn't touch the ball, it's a clear penalty.
"We didn't deserve to lose. In the second half we have a clear penalty and two chances more to score. It was very important not to concede another goal."