Describing it as "a big execution", former federal treasurer Peter Costello has effectively endorsed the leadership coup against Tony Abbott.

Key points: Former treasurer Peter Costello endorses Liberal leadership coup

Former treasurer Peter Costello endorses Liberal leadership coup Costello predicted "significant loss" had Abbott remained

Costello predicted "significant loss" had Abbott remained Says Liberal Party rewards success, not loyalty

Says Liberal Party rewards success, not loyalty Many of Abbott's budget measures "not worth" political capital

Mr Costello said it was "most certainly" the correct decision for the Liberal Party to install Malcolm Turnbull as Prime Minister.

Based on opinion polls since Mr Turnbull replaced Mr Abbott, Mr Costello said it appeared to have been the right decision.

He said that for the Abbott government "a significant loss was on the cards" and now "a significant victory" at next year's election was now a possibility.

Mr Costello made his first public comments about the change of Liberal leadership as part of a Four Corners program to air tonight.

The program examines the downfall of Mr Abbott and looks behind the scenes at the Turnbull coup.

In the days following the coup, Four Corners spoke to key powerbrokers and identities in the Liberal Party.

They included former party treasurer Michael Yabsley, campaign strategist Mark Textor, former senator Amanda Vanstone and key Abbott supporter Cory Bernardi.

Senator Bernardi brands the leadership change as "treachery".

Mr Yabsley said the "Credlin factor" — a reference to Mr Abbott's chief of staff Peta Credlin — was a major reason for the downfall of the prime minister.

"In so many respects, she came to have the role with the prime minister's colleagues that the prime minister should have had and this made her an extraordinarily powerful person," he said.

'Here's the rule ... if you win, you did the right thing'

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Mr Costello told Four Corners: "It looks ... the public have embraced it [the leadership change]."

Asked if Mr Turnbull did the right thing by seizing the leadership, Mr Costello said: "Here's the rule in the Liberal Party — if you win, you did the right thing.

"They're the rules of the Liberal Party. The Liberal Party really only rewards you for an outcome.

"If Malcolm had challenged and lost he would have done the wrong thing, but he challenged and won so the Liberal Party regards it as the right thing.

"The Liberal Party doesn't give you any great rewards for loyalty. That's not what it rewards, the Liberal Party rewards success."

Mr Costello said the decision to remove Mr Abbott was "very tough" but also "efficient".

"This was the execution of a first-term prime minister, [it was] very unusual in itself," he said.

"And the political execution of a first-term prime minister who was from the Coalition, the Liberal Party.

"[It was] extremely rare, probably unprecedented, certainly unprecedented, so you've got to say that was a big execution and a tough one."

Asked why Mr Abbott fell, Mr Costello said: "I think probably in the end it was the polls. That a majority of his colleagues felt that they were not going to win the next election and in those circumstances they decided to effect a change."

Abbott government's budget measures 'not worth political capital'

In the interview, Mr Costello criticised the Abbott government's first budget.

"I think the Government should have explained the problem more in advance," he said.

"It was elected in September [2013], it had until May to produce its first budget. You know, to me the task then was to explain and to level with the Australian people what the problem was."

Mr Costello said that budget should not have included measures which had no chance of passing the Senate.

"It just wasn't worth using political capital on them," he said.

"They might be right in principle like a Medicare co-payment, but if it were possible to do a Medicare co-payment, believe me, it would have been done a long time before now."

Mr Textor told Four Corners the major issue of concern among voters was that they did not understand what the Abbott government's economic strategy was.

"So perhaps if there is one thing Mr Abbott wanted to do again [it would be] to demonstrate more ... [adaptability] when it came to economic strategy," he said.

Mr Textor said the absence of a clear economic strategy created a "vacuum" which other "minor things" such as Bronwyn Bishop's helicopter ride, the Prince Philip announcement and same-sex marriage filled.

"So rather than those things being a distraction, I saw them as a symptom of people's concern about a lack of economically adaptive strategy that would take us forward," he said.

Four Corners: De-throning Tony Abbott program can be seen on ABC iview