Fernando Santos' men led through Nani in Saint-Etienne and appeared firmly in control at the break, before Birkir Bjarnason's goal levelled matters and Portugal were unable to respond.
Cristiano Ronaldo's comments criticising Iceland's "small mentality" after the match attracted widespread criticism, with Santos staunchly defending his talisman.
Portugal next take on Austria, beaten by rivals Hungary in a chastening setback last time out, at Parc des Princes on Saturday and Sporting Lisbon's Rui Patricio remains bullish over his team's prospects.
"Our confidence is always on top because we've managed to take the team this far and we know the quality we can put on to the pitch," he told a pre-match news conference.
"[The Iceland match] is not the result we wanted but we depend only on ourselves to reach our goals.
"The first goal is to pass the group stage. Our confidence has not been hurt. We know the quality of our game. We are going to do everything to win."
Portugal's display against Iceland drew its fair share of criticism from their supporters but Rui Patricio remains upbeat with regards to the backing they receive.
"We felt a lot of support and we feel very thankful for that support," he added. "People have been amazing, both here in France and also in Portugal .
"People are commenting on the matches and we feel all the stronger for that
"There is great pride in representing our country. No one has to congratulate me on stopping balls, everyone on the pitch tries to do their best.
"Whoever is playing is doing their best and who is on the bench is trying to propel us forward."