City needed to be patient as Villarreal looked to press them early on but once Toure had opened the scoring after 30 minutes, the result was rarely in doubt.
Mancini said: "Villarreal were missing four or five important players but it is always difficult to win away in the Champions League.
"We had 65 per cent of ball possession, we scored three goals. I think this was important for our confidence.
"I think we have improved, not just in the Champions League.
"It is important for us to go in the second stage, then everything can happen with us because we are a good team. We can improve a lot in the next month."