Giroud produced a neat close-range finish when turning in Lukas Podolski's cross to equalise at Upton Park, and is relieved to have got off the mark in the league.
Speaking to French broadcaster Canal+, Giroud said: "I expected it to be difficult at first because the Premier League is a level higher and I have had to adapt.
"It is nice to have scored my first goal, that will give me a lot of confidence for the future.
"I feel good about this team and I am confident that I will score more goals. Why not a dozen like in my first season at Montpellier?"