The Gills won the League Two title last season to secure a place in the third tier of English football for the first time in three years.
Allen believes that the Kent club will have no problem in making the step-up to League One level.
"Just about everyone here has done well at this level. League One ain't no great shakes, trust me," Allen told BBC Radio Kent.
"We are all on the edge of our seats thinking what will it be like playing against these big clubs? I honestly don't think they are that big.
"There are some good teams there and big clubs with big budgets, big stadiums and well paid players. But names are nothing and stadiums are nothing. Your history does not win out on the football pitch."
Gillingham begin their campaign at home to Colchester United on Saturday afternoon.