Mrs Brooks, who was cleared of phone hacking charges by an Old Bailey jury on Tuesday, told MPs on the Commons Culture, Media and Sport Select Committee in 2003 that police had been "paid for information in the past."
However, the former news executive's statement is covered by parliamentary privilege and inadmissable as evidence.
The former Labour deputy prime minister told the Lords it was a "matter of considerable concern", adding it was "probably not right" that privilege prevented the information being presented in court.
He added it "may have been right" before insisting the jury did not get "an important point that they should have considered".
Former Sun and News of the World editor Ms Brooks said on Thursday that she felt vindicated by the jury's verdict.
Lord Prescott won £40,000 in damages after journalists at the News Of The World hacked into his messages.