Allardyce made the claim following England's 3-2 victory over Spain in Seville on Monday, suggesting that Busquets, who has won seven LaLiga titles and three champions Leagues with Barcelona and a World Cup and European Championships for his country, was no better than Dier.
"The praise about Busquets... he's no better or worse than Eric Dier for me," he insisted.
"We laud him as a genius... Eric Dier was far better than Busquets last night."
However, speaking on 'The Debate', Allardyce admitted that he had over-egged his comments somewhat, insisting that he was merely trying to defend Dier against recent criticism.
"I slipped up a little bit, but on the night he was better than him.
"In career terms, he's not. But what I was doing was sticking up for Dier, after the amount of stick he's been getting.
"People saying he's not good enough for England, people saying he shouldn't be playing. There's been a lot of negative comments in the press."
Dier was given the sole responsibility of shielding the England back four with Jordan Henderson suspended and Allardyce was very impressed by his performance and not least his crunching challenge on Sergio Ramos after just 11 minutes.
"He plays it simple and sits in the right positions," Allardyce enthused.
"He made a great tackle [on Ramos]. That set a great standard for England on the night.
"In all fairness, you're not allowed to take the ball and the man anymore, but it was a good challenge to get everyone in the right frame of mind, like a good pass, a good header or a good shot. It put England on the front foot."