He scored the only goal of the game in the second half, taking La Roja's points tally to 28 from a possible -- the only dropped points a draw in Italy.
"I am really happy to play, to add to the team and in the end the goal was an important one for the win," Illarramendi said.
"Isreal were close together at the back. We tried to go wide but it didn't work out for us. In the end we managed to get the goal, though."
Thoughts now turn to next summer's World Cup: "It will be difficult because everyone wants to be there, but we will fight for it.
"Now it's time to return to my club and to work hard to be able to be in Russia."