"If we'd have met those standards and made those performances we would have been alright. But we fell below that and when you do that in top competitions you get punished.
"Iran posed a constant threat. We just could not get going and that really disappoints me the most."
Page said he was not happy with the team's performance even before the sending off of Hennessey, who became the first player at this year's World Cup to pick up a red card.
"We want to finish the competition on a high, if it is in our hands to go through. We want to finish with a good performance and a win," Page added of Tuesday's England game.
"We are low at the minute but we are going to get back up tomorrow and get ready for another tough game."
Captain Gareth Bale, who became Wales' most-capped player with 110 appearances, said the players were gutted.
"It is going to be difficult for us for sure. We will have to see. What can I say? We recover and we have to go again," said the 33-year-old, who had little impact in the Welsh attack.