Mr Carpenter was yesterday forced to sack Small Business Minister Norm Marlborough from cabinet after the state's corruption watchdog revealed evidence of secret dealings he had with Mr Burke.
The Corruption and Crime Commission (CCC) revealed phone records and tapped phone recordings between Mr Marlborough and Mr Burke, in which the minister agreed to appoint a woman to a board at Mr Burke's urging.
Mr Marlborough also took instructions from Mr Burke about how to respond to questions in parliament, and lied to the CCC about his links to the former premier, who was jailed in 1994 for travel rorts.
Mr Carpenter today said Mr Burke had to leave the Australian Labor Party.
"I just think that what we have to do now is to purge from the Labor Party of the influence of Brian Burke," Mr Carpenter told ABC Radio.
"The Labor Party has to decide whether it wants to go down in a screaming heap caused by Brian Burke, or it wants to be a credible party which can produce credible government doing good for the community of Western Australia."
Mr Carpenter said the party had to choose between him and Mr Burke.
"I expect the Labor Party to make the choice and if they make the wrong choice then there's no future in it for me."
The affair has revived the spectre of Labor's disastrous WA Inc era of the 1980s, when the Labor government under Mr Burke became involved in major business dealings with businessman including Alan Bond.