The Peru international, 26, has made just four appearances in two years after arriving from Coronel Bologensi.
He has now returned to Peru in a bid to resurrect his career in his homeland but paid tribute to the Clarets' first-choice stopper Brian Jensen.
Penny told burnleyfc.com: "I will never forget Burnley because it was a great step up for me.
"I am sad I didn't play more times. I think in football the most important thing is playing regularly but I tried to do my best every single day and Brian has been outstanding during my time with the club.
"It didn't happen for me but I do think I pushed Brian to be the best he could and Burnley have benefited from that."