"It was tough for me, but it was amazing to sign for a club like Chelsea. It was like an improvement for me because - OK, it's Manchester City now - but Chelsea have been the best club in England over the past 10 years.
"It was a new challenge with big motivation, big targets."
After 19 consecutive seasons in the Champions League, Arsenal face a third year in the Europa League and are operating with a restricted budget in the transfer market as a result.
On Monday, a group of 16 prominent supporters' groups and bloggers signed a letter calling on Gunners owner Stan Kroenke to "reinvigorate" the club.
Giroud expressed sympathy - "I can understand the fans" - and said there is perhaps a difference in mindset between his previous and current employers.
"With Arsenal it was difficult to fight for the title. We were always fighting for the Champions League places," he said. "I won a few FA Cups and Community Shields. When you can't win the league, winning the FA Cup is quite nice, so I've got amazing memories.
"Chelsea is a club where you have maybe more expectations, higher expectations. They were winning more titles these past 10 years and obviously Arsenal wants to come back to the 'Invincibles' days, but it's not easy.
"I'm not going to say we are doing things better at Chelsea. We just try to be as competitive as we can, to step up and win more trophies."
When asked if it could be a mentality issue, Giroud replied: "Maybe.
"In football, for me, it's two-thirds of the quality you need to have. I've seen so many talented players - but without mental strength they can't step up and get out of their comfort zone. Mental strength is massive in football and sport in general."
