"I congratulate Barcelona, they have played a very good, very serious championship," said the Spain goalkeeper during the presentation of his new official website and Facebook page.
"I congratulate them, on behalf of myself and Real Madrid, as they showed themselves to be very respectful when we won the King's Cup (by beating Barcelona 1-0) a few days ago."
Casillas also sought to diffuse the tension that had built up between the two teams during the four hard-fought 'clasicos' that they contested with each other in recent weeks.
"After 20 days of such confrontations with Barcelona, it's normal that there was tension but we have to forget that and turn the page," said Casillas, who won the World Cup with Spain alongside several Barca players last year.
The Real goalkeeper added that he would be supporting "football" when Barca meet Manchester United in the Champions League final at Wembley in London on May 28.
Barcelona sealed victory in this season's Spanish title race by drawing 1-1 at Levante on Wednesday evening.