Cohen defended the performance of both axed shows in an interview with the Radio Times.
"I wouldn't describe them as flops," he said. "I don't like to throw around words like that about individual programmes.
"I embrace the fact that not everything works because if nothing fails, then you're not taking enough creative risks. It's important that the BBC, as a public service broadcaster, takes those risks."
Cohen also dismissed the suggestion that long-running sitcom My Family had been dropped because it was too "middle-class".
"Not true," he insisted. "Every comedy reaches the point where it's not as fresh as it was. The family had fled, they'd left the house!"
Defending his decisions, Cohen added: "There's only a finite amount of money and, by ending some shows, I freed the money to do Call the Midwife in January. That's how it works."
The Royal Bodyguard aired for a single series throughout December and January, while Upstairs Downstairs was axed in April.