The new BBC One talent show, which stars Sir Tom Jones and Jessie J as coaches, surprised the long-running ITV1 hit and actually beat the Cowell show during some of the audition rounds.
However, Got Talent increased its figures during the Live Shows and ended up beating the BBC series overall across the run.
Speaking about Cowell's response to the new rivalry, Greene claimed that in the long run, Syco was pleased with the fresh competition as it helped them up their game.
"For me, competition is brilliant. That really focused our mind. We produced a series that was even better than it was going to be because of The Voice," said the TV boss.
"Was Simon nervous? No. For all of us, it focused the mind. Competition is healthy and strong."
Going into more detail about the weeks when BGT was losing the ratings war, she said: "I was eating chicken pie three times a week and Simon's watching the show doing the editing. He was focused. We always ate chicken pie. Brenda makes the chicken pie.
"We had already shot all the show and all the auditions, we didn't change anything we did, we just had a keen focus to keep our foot on the gas. The show's always changing anyway."