Giuseppe Rossi netted the only goal of the game with a 71st-minute penalty as Villarreal bounced back from successive league defeats to Barcelona and Valencia to further strengthen their hold on fourth place.
Garrido said: "I'm very happy. On a personal level, it's nice (reaching 50 games), although my aim is to have many more games with Villarreal.
"It's nice to celebrate it with a victory. We know that by competing in other competitions we haven't picked up as many points as we would have liked, but with this triumph we have moved closer to our objective.
"As I said before, it was a vital game to keeping intact our intact of finishing in the top four. There aren't many points left to play for. It's a step more, and important step, and although there are several more to take, this victory was key.
"We knew that it was going to be difficult, a victory we were going to have to suffer for, because Zaragoza are a difficult team who are a having a great second half of the season with good players.
"We had a good first half in which we could have gone into the break with an advantage and in the second, we scored, we suffered, but we worked as hard as possible."