The 31-year-old has had a shaky start to the season, as have his team, who have already slipped seven points behind leaders Barcelona.
They have a chance to pick up just their fourth La Liga win of the campaign against Celta Vigo at the Bernabeu tomorrow [Saturday] and Casillas says the negative voices are not affecting him.
The Spain number one told Madrid's official website: "You take it (the criticism) with a sense of humour.
"You have to respect people's right to criticise. As long as it's constructive criticism, it's a positive thing.
"When you've been at the top and in a club like Real Madrid this long you know that in two or three matches things can change.
"I've been living many years with this. You have to keep going and try to turn those dissenting voices around."
Madrid face a testing five days with tomorrow's [Saturday] clash followed by a Champions League trip to German champions Borussia Dortmund.
They have injury concerns at the back ahead of the game with 12th-placed Celta, with full-backs Marcelo, Fabio Coentrao and Alvaro Arbeloa definitely out and doubts over a number of other players following their international exertions.
Raul Albiol is one of those looking to step in and the defender offered his support to Casillas, saying there was a campaign to stop him winning the Ballon d'Or.
"This campaign is to make one less problem for those who choose the Ballon D'Or," he said on www.marca.com.
"Clearly for a goalkeeper to win the award is very difficult, but if anyone can do it it is Iker. Last year, he won trophies with Spain and with Real Madrid. He had a great season."
Celta goalkeeper Javi Varas, who is unlikely to feature tomorrow because of illness, has also come out in support of Casillas, calling him the "best goalkeeper in the world".
He told EFE: "The criticism Casillas is getting is unfair, but usually a goalkeeper's mistakes are the ones most commonly seen.
"We are talking about the best goalkeeper in the world, a reference point for all Spanish goalkeepers, including me."
Varas said it was "disrespectful to doubt the professionalism of a player who has given so much joy to both club and country."
Varas' place in goal against Madrid could be taken by Ruben Blanco.
Natxo Insa is definitely out, while forward Park Chu-young is a doubt after returning from international duty with South Korea with a leg problem.