Goals from Jamie Paterson and Lars Veldwijk secured Forest's place in tomorrow night's third-round draw and Montanier says his side's victory at The Den is another sign of his team's progression.
Speaking after the game he said: "It's not the best game that we've played but getting into the next round of the cup is important. It was a very similar game to the one at Doncaster and I think the players showed great commitment to get the win as we did that night.
"We should have had a clean sheet but Millwall scored a fantastic goal. However, we showed great character to come back and win the game at the end and that was important because we wanted to avoid extra-time to keep ourselves fresh for Saturday."
Montanier handed a senior debut to 20-year-old James Thorne and while the head coach was positive about his young striker's performance, he also had good news about one his more senior players.
He said: "The door will always be open for players from the academy. James Thorne came into the team tonight and although it was difficult for him, he must continue to learn and work hard to get himself into the team on another night."
"Britt's injury is not very serious. We're hopeful that he could play against Leeds on Saturday but we're not sure yet. We're obviously very pleased for him because we know it could have been a lot worse."
Tickets are still available for the next home game against Leeds United via tickets.nottinghamforest.co.uk, in-person at the ticket office or by calling 0115 982 4388.