Higuain struck Madrid's opening two goals and, after Tenerife pulled a controversial goal back through Ayoze Garcia just after half-time, he then set up Kaka to make it 3-1.
Cristiano Ronaldo, from the penalty spot, and substitute Raul added further goals in the final 10 minutes.
Pellegrini said, "There is always room for improvement, we are not yet perfect.
"We still need to hold on to the ball better, but with our continued effort, it will soon happen.
"We won because we worked hard for the whole game."