Liberal Democrat leader Nick Clegg challenged Mr Brown to prove he really was "a listening prime minister" by halting the closure of post offices
Mr Brown said the Lib Dems were again "proposing to spend huge sums of extra money without having any recognisable means of paying for them... that's why your shadow home secretary called you Calamity Clegg".
The government announced last week it would compensate those affected by the 10p tax change, amid pressure from Labour MPs.
Mr Brown announced the abolition of the 10p starter rate of income tax in his last Budget as chancellor, last year.
He told BBC Radio 4's Today programme on Wednesday this had helped the poorest in society most "because 85% of the benefits [of the old rate] went to the highest earners".
It wasn't quite Roy Scheider in the final scenes of Jaws, but it was a confident punch on the nose
However, he added: "We made two mistakes. We didn't cover as well as we should that group of low-paid workers who don't get the working tax credits and we weren't able to help the 60 to 64-year-olds who didn't get the pensioner's tax allowance."
Mr Brown also said: "The problem was quite specific... We had dealt with this very, very major tax reform. We hadn't done enough for these two smaller groups."
In the last year, the prime minister said, rising fuel and food prices meant "the context in which we are having to make decisions now is quite different".
Ministers saw off a potential Labour backbench revolt by pledging concessions last week for those hit by the 10p tax rate abolition.
These are to be outlined over the next few months.
Earlier, Brown told BBC Radio 5 Live: "If I have been accused of not listening in the past, I'm listening and I'm learning all the time.
"I think one of the things about this job is you learn all the time from the difficult decisions you have got to make."
Asked whether he had a "presentational problem" and was less able to give a "human answer" to a question than predecessor Tony Blair, he said: "My job is to work every day on behalf of the people of this country.
"I think people are less interested in the theatre of it and less interested in the personalities."
On Tuesday, Bank of England governor Mervyn King called for an end to excessive City pay packages and blamed the City and its bonus culture for the credit crunch.
'Quicker the better'
Mr Brown told Today: "We've had excessive risk-taking and at the same time we've now got risk aversion.
Gordon loathes talking about himself which seems merely to fuel the media's delight in doing just that
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