Operatic singer Jonathan Antoine was initially told by Cowell to drop Charlotte Jaconelli from the lineup, but the pair eventually went on to finish as the show's runners-up.
The duo are now signed to Cowell's record label Syco, and will release their debut LP Together on September 24.
"We had a meeting with him, he made a little apology," Jaconelli told BBC Breakfast.
Antoine joked: "Like a Simon Cowell apology. The word 'sorry' wasn't actually involved, but the implication was there."
The 17-year-old also revealed that he may attempt to break into professional opera in the future.
He said: "I would at some point like to be in an opera, but it would take years of studying."
Jaconelli added that the pair have no hard feelings over Talent winners Ashleigh & Pudsey, saying: "Ashleigh & Pudsey are so lovely you can't have any negative reaction to it."
Together will feature covers by artists including Take That and Elton John alongside new songs.
Jonathan & Charlotte will star in their own one-off documentary on ITV1 on November 6.