The 33-year-old barely started during an ill-fated Celtic spell.
Highly-rated Hibernian striker Riordan joined the Hoops in 2006 but managed just 24 Premiership appearances throughout his two-year stint at Paradise.
Strachan had once described the 33-year-old - who managed five Premiership goals in eight starts for the Hoops - as one of the most natural finishers he had ever seen.
However, the duo had a high-profile falling-out, but Riordan wonders why his minutes on the pitch were as limited as they were if the Scotland boss meant what he said in relation to his ability.
"I could have gone to a number of clubs but half of my family were huge Celtic fans so it made sense," he told BBC Sport.
"I didn't play as much as I wanted and then I had the fall out with Strachan - I just wanted to play. If the manager thought I was the best finisher he'd seen then why was I not playing?"
Riordan returned to Hibs for the 2008-09 season, netting 12 top-flight goals in 28 starts to restore his reputation as a goalscorer following his Celtic troubles.
He netted 25 league goals over the next two seasons, before his career declined somewhat after joining St Johnstone, Alloa and Bristol Rovers. Riordan is currently a free agent.