The winger won a decisive penalty to eliminate Mexico, but the goalkeeper has backed his team-mate's claims that his fall was legitimate
With the matched poised at 1-1 and having entered stoppage time, Robben was awarded a spot-kick after going down under a challenge from Rafael Marquez, and while the Bayern Munich star claims he was fouled by the Mexico captain, his admission that he dived earlier in the match has caused a stir.
Cillessen, however, has backed up his international team-mate's claims, insisting the decision of referee Pedro Proenca was correct.
"He doesn't go down that easy, and I think we should have had a penalty in the first half," he said. "I've not seen it back, but I think it's a penalty. If he says it's a penalty, I believe him."
Regardless of the late nature of the Dutch victory – Wesley Sneijder's equaliser arrived in the 88th minute – the Ajax shot-stopper was confident his side could pull through, aided by the contribution of Klaas-Jan Huntelaar, who came on as a substitute to score the late penalty.
"We kept confidence and we knew if we scored before the end of the game we'd go on and win it - and that's what we did," he said.
"We have a great bench, full of players who want to play. We saw that from Leroy Fer against Chile and Memphis Depay against Australia. We have a great team."
The weather was a major discussion point before the match, and though the 25-year-old admitted that conditions were not easy, he was pleased his side came through such a challenge.
"It was warmer than where we trained, but we trained here for two days. It's not our favourite kind of weather, but we showed we can win here," he continued.
"We had belief, and we believe it can get better, especially when you can win in this kind of situation, with this weather and we think we can beat everyone."
Netherlands will face the winner of Greece and Costa Rica in the quarter-finals next weekend.