The France forward played in La Paillade's 2-1 victory over Auxerre on Sunday that secured the title, where John Utaka grabbed both goals to ensure the side finished the season top of the table three points clear of nearest rivals Paris Saint-Germain.
“It is exceptional for Montpellier [to win the league],” the striker told L'Equipe. “We really wanted to live the moment.
“The match was not easy, but we managed to stay in the game. Everyone had to be strong mentally and remained focused.”
Central defender Henri Bedimo, who was suspended for the clash, was also quick to congratulate his team-mates after the final whistle.
“It was hard for me to watch the game,” the Cameroon international told Canal Plus . “I'm trying to get over the emotion of it all.”
“The guys did the job. With all that was going on, it was not easy to stay focused.”
Montpellier won Ligue 1 for the first time in their 38-year history with 82 points. Giroud meanwhile, finished as joint-top goalscorer alongside PSG's Nene with 21 strikes to his name.