The Gunners have not won a trophy since their FA Cup triumph of 2005, and their wait for a top-flight championship stretches back a further year.
Thomas thinks that Arsenal are an improved outfit since last season, but still feels their lack of a Patrick Viera-like holding midfielder will see them come up short in their quest for top honours.
"[Santi] Cazorla is a fantastic player but I think they need someone to shut the gap - a holding midfielder in the style of Patrick Vieira to run the show. Sometimes they are a bit brittle and haven't got the mindset to last the whole season," Thomas told BBC Sport.
"I don't think they have the steel to win major trophies. Manchester United, Chelsea and Manchester City will go to the end and contest things.
"It's all about your mentality. I don't think Arsenal are hardened enough to win a title. It's down to Arsene Wenger to change that. They are always going to play great football, but there is something missing from the jigsaw."
Thomas made over 200 appearances during a seven-year spell with Arsenal, twice winning the old First Division title.