The former bosses, along with other bankers, have been criticised for taking huge bonuses from banks that later had to rely on taxpayer money to survive.
Separately, the Tories demanded an urgent inquiry into claims that one of Gordon Brown's key advisers, Sir James Crosby, sacked HBOS executive Paul Moore, who warned about excessive risk taking.
Sir James, who was HBOS' chief executive at the time and is now the deputy head of the Financial Services Authority, allegedly sacked Mr Moore in 2005 after he warned the bank's board about its potentially dangerous "sales culture".
"The bonus system has proved to be wrong. Substantial cash bonuses do not reward the right kind of behaviour," he said.
Sir Tom McKillop agreed that a fundamental review of remuneration was needed.
But when asked whether the bonus culture encouraged excessive risk taking and had exacerbated the banking crisis, Sir Fred Goodwin argued that traders had been trading within set limits, and had simply been doing "what they were authorised to do".
It is "hard to say that remuneration was a cause [of the bank's problems]," he said.
Sir Fred oversaw a number of acquisitions that made Edinburgh-based RBS one of the world's biggest banks.
Former chief executive, HBOS, 42
Salary: £1.93m, including bonus and benefits (2007)
Joined HBOS from Asda in 1999
Resignation announced in October 2008
But his £10bn deal to buy Dutch rival ABN Amro late in 2007 is now seen as ill-timed and a deal too far in light of RBS's inability to survive the credit crunch without a massive injection of government funds.
Sir Tom admitted to the committee that the deal to buy ABN was "a big mistake".
"We bought it at the top of the market and anything we paid was an error. We are sorry we bought ABN Amro," he said.
Sir Fred said it was a "bad decision and certainly mistimed."
He said the size of RBS, together with its lack of cash following the ABN Amro, made it particularly susceptible to the credit crunch.
RBS is now nearly 70%-owned by the taxpayer after a government rescue package was put in place at the end of last year.
No easy ride
The ex-bosses of HBOS also admitted mistakes.
When pushed, Lord Stevenson, former chairman of HBOS, said the mistake the bank made was a failure to predict the credit crunch, which effectively froze access to new funds.
Former chairman HBOS
Salary: £821,000 including benefits (2007)
Resignation announced in October 2008
"The fundamental mistake of HBOS was the failure to predict the wholesale collapse of the wholesale markets," he said.
The MPs asked why a HBOS group risk manager was sacked in 2005 for raising questions about the levels of risk the bank was taking on.
Lord Stevenson would not be drawn on the specifics of the sacking, simply saying that it had been subject to an independent investigation.
But Mr Hornby stressed that an over-reliance on wholesale capital markets for funding was indeed the root cause of the problem.
"We were over-exposed to wholesale funding," he said.
Banks use the wholesale markets to raise cash - effectively borrowing money from other financial institutions.
When this funding dried up as a result of the credit crunch, the bank was left high and dry, he and Lord Stevenson argued.
HBOS was rescued by Lloyds and the merged group is now more than 40%-owned by the government.
The bosses still in place at the helm of Britain's leading banks will appear before the Treasury Committee on Wednesday.
Bosses' pay at UK banks receiving government support
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