The 26-year-old, who started his career at Brentford, joined the Grecians last summer after a spell with seventh-tier Hayes and Yeading.
He told BBC Radio Devon, “My brother told me to ring the manager and just see what happens.”
“If it was not for my brother I probably would not be here today.”
He continued: “Thankfully I have turned that corner and am now here.”
Cole, who has made 36 appearances this season, leads St James Park in goals scored with five and has rapidly grown to be a fan favourite.
“I had not lost all belief but I was going down that path where I was done with football,” he stated.
“I assumed that was the end of my football career, so it seems strange to be sitting here talking to you guys today because in football, those opportunities don’t come along very often.
“I had not lost all belief but I was going down that path where I was done with football,” he continued.
“I thought that was me done with full-time football, so for me to be sitting here today chatting with you guys is surreal because you just don’t get those chances in football really, once you are out of the game you are out of the game and it is hard to get back in.”
Exeter City, who hosted Charlton on Friday, won their next two League One games prior to the international break.
