Cole won a free kick in the first half of yesterday's fifth-round replay at Stamford Bridge after going down following a tussle with Bees defender Shaleum Logan.
The England left-back fell to the ground clutching his chest despite replays showing that Logan made little or no contact with the Chelsea defender.
Wright was working as a pundit on the match and believes that Cole deliberately exaggerated the incident to win a set piece for his side.
He told ITV Sport: "He's not touched him, he's nicked something off the referee there. It looks like he's touched him but he's not. He's acted like he's hurt but he's not hurt.
"It's worrying to see that this is something so natural in the game now. I hate to see it. It's horrible.
"It's something that's coming into the game more and more and you can't blame the foreign players any more."