Tim Krul came on in the dying stages of the Netherlands' FIFA World Cup quarter-final win over Costa Rica, specifically for the penalty shootout during which he made two saves.
Cillessen, who kept a clean sheet through the best part of 120 minutes in the 0-0 draw before the 4-3 shootout win, said he remained confident as always.
Asked if his confidence would be affected in a big game, the 25-year-old Ajax shot-stopper said: "No, not at all.
"Why should it? We trained on it. The coach in that moment had more confidence [in Tim] so during a game I would have to prove that I can do it also.
"And then we have to make sure we don't go to penalties next time."
Despite Krul's heroics, Cillessen is expected to retain his starting spot for Wednesday's semi-final against Argentina at the Arena de Sao Paulo.
Cillessen said the absence of injured Argentina star Angel di Maria would make no difference to his team.
"He's a good player but we look at the whole team, not one player," he said.
"So tomorrow we are going to watch how Argentina play and we're going to make our plan to beat them."
