The decision has been condemned by the Football Supporters' Association, while some fans have launched a petition urging the broadcaster to re-think.
However, responding to what it described as "some complaints" - the the corporation received around 250 - the BBC has elaborated on its reasons for dispensing with a long-standing feature of its Sports Report show.
A statement said: "We appreciate the strength of feeling towards the classified football results within Sports Report. It's always difficult when a programme with a special history changes, but there are good reasons for the change.
"With the addition of the 5.30pm live Premier League match to our coverage, Sports Report has been condensed into a shorter programme - cut from 1 hour to 25 minutes. The classifieds were taking around 5-7 minutes to read, which would have taken up around a third of the programme - constraining the range of sport we could cover.
"We'd like to assure our listeners that results from across the football leagues will still be shared during the programme and through the afternoon. Results are also available in full on the BBC Sport website and during Final Score on BBC One. Having a live match at 5.30 is a great addition to the 5 Live schedule."
James Alexander Gordon became a household name as he read out the day's scorelines to listeners for 40 years before Charlotte Green took over when he stepped down in 2013.
The petition urging the BBC to retain the classified results says: "Though scores are available online, mobile, and on the TV, there has always been the tried and trusted method of getting in the car, or listening to the radio on the move.
"If your mobile coverage fails you (as it often does in congested football grounds), there is always Sports Report to tell you how the rest of the football pyramid fared today.
"Sports Report is indeed a shortened affair these days, but as fans, we would prefer to sacrifice a manager's interview than do away with an institution that has served us and the footballing world for decades."
However, by late on Wednesday afternoon the petition had attracted only 71 signatures.