Brawn rescued the team from collapse after Honda's withdrawal at the end of 2008 and guided it to a double championship triumph in 2009 before selling it to Mercedes.
He left the team at the end of 2013 due to disagreements with Lauda and Toto Wolff.
"He refused to work with Paddy Lowe," team chairman Lauda told Die Welt newspaper.
"It's a pity that it happened," he added. "But judge for yourself.
"When he left, Mercedes immediately took second place in the constructors' championship, and then won three titles in a row. I have nothing more to add," said Lauda.
Brawn was actually still part of the team when it finished second in the 2013 standings, although they did go on to win three consecutive constructors' and drivers' titles in the following years.
Bahrain International Circuit - Winter testing