The Dutch cost his team two valuable points after his reckless challenge on Royston Drenthe resulted in an injury time winning penalty for Real.
"It was a correct penalty as I arrived a bit late in tackling Drenthe," Heitinga was quoted as saying by Marca on Monday.
"I'm really sorry for the team and the fans alike but these things happen in football."
Despite losing three league games in a row, the 24-year-old centre back issued a public support for coach Javier Aguirre.
"Aguirre is a very good coach and he did a great job last year by earning the club a UEFA Champions League spot."
After back to back league games against Barcelona and Real Madrid, Atletico will next be up against Liverpool in an important Champions League tie.
"Liverpool are a very strong side. They are Champions League regulars and made the final twice in the last four years."
"We will be playing at home and we'll strive to achieve a victory," concluded the former Ajax man.