Captain Alastair Cook was rebuffed by Australia skipper Clarke after England's 169-run win on Saturday, though the match was played in good spirit.
Anderson said England and New Zealand had shared a drink after each hard-fought match of their drawn test series earlier in the summer and Cook had wanted to continue the ritual with Clarke's team.
"It was Cooky's idea and he went and asked them after the game," Anderson told British media.
"We were all happy to do it. I don't know why they didn't come in. Maybe they wanted to carry on doing things their way. You'll have to ask them. It's their prerogative.
"We had a beer with the New Zealand team after both tests and we found it an enjoyable thing to do after a hard test.
"It didn't matter whether we won or lost, we did it and it's something we want to carry on doing."
Win, lose or draw, Australia and England once shared a drink after the final day's play of each test but Ricky Ponting put paid to the tradition after his team lost the 2005 series.
The hard-bitten Tasmanian felt his players may have lost their competitive edge by being too friendly with their opponents and since, the teams have generally held off mixing with each other until the end of a series.
In contrast to the tetchy 2013/14 series in Australia, where the hosts won 5-0 and both teams engaged in some heated exchanges out in the middle, the Cardiff test passed without incident.
"The spirit was different from our point of view because we weren't fussed about trying to start any battles," Anderson said.
"We were really focussed on what we were going to do and when you rack up runs generally the opposition are quiet whoever you're playing against."
(Writing by Ian Ransom; Editing by Greg Stutchbury)
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