Inverdale sparked complaints when he plugged the tennis tournament as he presented the Ireland v Scotland Six Nations Rugby match on BBC1 earlier this month.
But the BBC said that Inverdale - who got into hot water last year when he said that Wimbledon champion Marion Bartoli was ''never going to be a looker'' - made the slip unintentionally.
It said: "We received complaints from viewers who were unhappy with a comment made by John Inverdale during the Ireland v Scotland match.
"Some viewers felt his reference to England, rather than Great Britain was inaccurate and biased.
"John made an unintentional slip despite clearly knowing that it is Great Britain and not England that competes in the Davis Cup.
"He apologised for his mistake later in the programme once he had realised his error."
Talking about the Davis Cup, Inverdale had told viewers: "If (Andy) Murray wins, England win a group match in the Davis Cup for the first time since 1986."
The sports broadcaster provoked controversy last year when he said that Bartoli was ''never going to be a looker".
He told listeners on Radio 5 live: ''Do you think Bartoli's dad told her when she was little, 'you're never going to be a looker, you'll never be a (Maria) Sharapova, so you have to be scrappy and fight?'"
Culture Secretary Maria Miller raised concerns with the BBC over the ''derogatory'' remark.
BBC director-general Tony Hall said that he found the comment ''totally unacceptable'' and that it fell below expected standards.
Inverdale apologised and said that the remark was "clumsy" and "ham-fisted".