The case, being heard at the capital's High Court, concerns an article that appeared in The Evening Standard newspaper on 11 April last year.
Mr Cleese's QC Jonathan Caplan told the court that the thrust of the article was that the comedian "emigrated to the US where he has become a humiliated failure".
Adrienne Page QC, for the newspaper, told the court that the matter "should have been settled in August last year at £10,000".
"There is no justification for greater compensation to be rewarded," she said.
Speaking via video link from his home in California, Mr Cleese told a judge in London he rejected the offer of £10,000 from the paper because he regarded its published apology as insufficient.
He added that it had also not been put in a "sufficiently prominent" place in the newspaper.
Mr Cleese, 63, told the court he had formed the impression the paper was not "genuinely sorry".
"I found in the past that when there is a nasty attack like this, one's first reaction is to feel bewildered and disorientated and, to a certain extent, scared," he said.
'Lifetime achievement'
Mr Cleese was watching the proceedings from California in what was, for him, the early hours of the morning.
He had earlier listened as Mr Caplan told the court the article "struck at the core of Mr Cleese's lifetime achievement".
The judge will give his ruling in the next few days.