After lifting La Liga trophy last season, Mourinho has found life tough this time around with Madrid already 11 points behind arch-rivals Barcelona.
Added to their woes is the fact that neighbours Atletico are riding high in second place with star striker Radamel Falcao stealing all the headlines.
That has put the heat on Mourinho, who was booed by sections of the Bernabeu crowd during Tuesday's Copa del Rey win over second tier Alcoyano.
Madrid lost 1-0 at Real Betis last weekend, meaning they have now dropped one less point than for the whole of last season, to leave them in the unusual position of trailing their city rivals ahead of a derby.
Casillas admits his team can afford nothing less than victory this weekend, and eat into an eight-point gap, and believes Mourinho is the man to turn their fortunes around.
"It (the fans' booing) may be unfair on Mourinho. He took on a new team with young players. Much of the success has been down to him, we have had some very good seasons recently," he told reporters.
"He is the best coach in the world and has shown this.
"Our trust in him is absolute. Mourinho is a coach who has given us much. Barcelona were playing well and went on to win titles and over those seasons defeated us. Last season the clear favourite was Barcelona.
"We hope to continue to regain ground in the league. We thought we might be closer going into the derby if we had won in Seville, but it cannot be and we will try to now make it a five-point gap with the derby.
"Right now, both teams are ahead of us. In recent years we have been fortunate to have gone unbeaten against Atletico, but that does not mean anything when we are looking for nothing but a win. The draw is worth nothing to us."