The Reds found themselves behind twice inside the opening 14 minutes at Oakwell, but they showed great character to battle back and secure the points, with midfielder Henri Lansbury scoring a hat-trick.
Montanier conceded after the match that he was disappointed by his side's slow start, but he was delighted with the way they battled back to claim the victory.
He said: "I wasn't especially satisfied after the first 20 minutes we played, but after that it was a good reaction. We were efficient and I'm very proud as always of our squad."
Forest have now won back-to-back Championship matches for the first time since August, and Montanier is now hoping his side can kick on during the busy festive period.
"We now have two successive victories and we needed to win because our position [in the Sky Bet Championship table] is not good," the Frenchman added. "After [beating] Ipswich we played well, and it was important to win this game."