An innings triumph over Durham secured the title on Friday, and Gillespie believes that the number of comfortable wins recorded shows that there wasn't a match for his side.
"We believe that we have played some really strong cricket this year and the lads deserve it," the former Australian bowler told BBC Radio Leeds. "We were ruthless.
"To win five games by an innings is an amazing effort.
"It's one of the best moments in my career. I had some great times in my playing career and really enjoyed it and now this is the peak of my coaching career. It's a fantastic feeling."
Yorkshire have won the County Championship on 31 occasions.