Peru coach Sergio Markarian slammed referee Patricio Loustau for sending off Victor Yotun for a clash with Suarez in the first half at the Estadio Nacional de Lima.
The Uruguay forward theatrically fell to the ground following the clash with Yotun who was shown a straight red card.
Marakarian told reporters: "I'll do my best to make sure this referee does not go to the World Cup because I'm not ashamed to say it was totally decisive [in the result].
"What Yotun did was silly but I've seen worse, like elbows or persistent simulation that goes unpunished."
Four minutes earlier Suarez earned his side a penalty - from which he scored - when he went to ground following a challenge from Christian Ramos, though, replays showed there was minimal contact.
Liverpool's striker is currently serving a 10-match ban for biting Chelsea defender Branislav Ivanovic.
Peru are now five points behind Uruguay, who occupy the fifth-place play-off position in the Conmebol qualifying pool.