Speaking to BBC Radio London after the 0-1 defeat to Brighton and Hove Albion, Gibbons spoke of the team's desire to assert themselves in the WSL.
She said: "I think there are a lot of people who have written us off already, but we have come up, and we're here to stay.
"We don’t want to just make up the numbers, so we're doing everything we can. There were a lot of changes over the summer with new signings that have added a lot of quality to our squad, and we're all working hard on the training pitch to ensure we don’t go back down."