Wales had to survive some scares on a nervy night at the Cardiff City Stadium but, in the end, Grainger’s side managed the game superbly to book their play-off spot.
Head coach Grainger said: “I’m so happy for the players. That performance they put in, they deserve everything they got.
“We wanted to deliver the game plan and they did that.
“I knew from the moment the players arrived at the stadium the levels of concentration they had.
“That they executed that is the next step for us as a team.”
Wales started slowly with Slovenia skipper Mateja Zver twice going close to silencing a record 12,741 home crowd.
But skipper Sophie Ingle and Carrie Jones had first-half chances and Wales were on top by the break.
The pattern continued in the second half and Jones had a strong penalty appeal turned down before Gemma Evans’ close-range header was pushed away by Slovenia goalkeeper Zala Mersnik.
Grainger said: “I think in the first 20 minutes we took time to settle, it was the same for Slovenia.
“But we grew into the game and by the end of the first half I think our plan was clear.
“We’ve created some very good chances, but ultimately we wanted to get a clean sheet and that’s what we’ve done.
“Overall I felt we had the better chances and managed the game well, and our objective has been met.”
Grainger will attend Friday’s play-off draw in Switzerland.
The ties will consist of a semi-final and final, each one leg, to be played on October 6 and October 11.
Wales will be involved in the first round of semi-final games with five other sides.
The three teams with the best qualifying records will be waiting for the three victorious semi-finalists at the final stage.
“One of the mistakes that teams can make in qualification campaigns is talk about things before they happen.
“But you can see when we play friendly games we play against higher-ranked opposition because that’s who we want to face.
“We know that we want to be a tournament team and we want to put in performances like we did tonight.
“From last September (the opening qualifier against Kazakhstan) we’ve built gradually, and we want to keep doing.”