The Hoops won the Scottish Premier League and the Scottish Cup last season as well as making it through to the last 16 of the Champions League.
Despite a continued flow of silverware at Parkhead, Brown believes that Lennon does not get enough praise.
"He's due a bit more recognition," Brown told the Daily Record. "Everyone thinks it's easy here and we should win the treble and have a run in the Champions League, but we play 60 or 70 games a season, so to be consistent is difficult."
Celtic begin the defence of their SPL title at home to Ross County on August 3.