Barry-Murphy took over the Spotland reins from Keith Hill in March 2019, having previously been part of the coaching staff.
Following an 18th-place finish last season, the Dale are currently rooted to the bottom of the League One table and four points adrift of safety.
Barry-Murphy was rewarded with a contract extension until the summer of 2022 before Christmas – although Rochdale failed to make the news public.
However, after the Greater Manchester outfit’s form dipped following the turn of the year, the Dale said Barry-Murphy penning fresh terms became 'difficult to announce’.
A statement from the board of directors said: ‘We understand supporters’ frustration with results and off-field decisions, and we admit that communication could and should have been better throughout the season.
‘Brian, who is a hugely talented manager, has worked at Rochdale AFC for 11 years and the board of directors are fully behind him and his team. He is under contract until the summer of 2022, having signed an extension before Christmas.
‘Unfortunately, results ultimately dipped as we entered into January and it became difficult to announce the news.
‘We admit and accept that the news should have been communicated at the time when Brian signed the extension, and we can only apologise that it wasn’t.
‘We now have a break in fixtures, with the team next back in action on Good Friday, when we take on Portsmouth at Fratton Park, in the first of our 10 remaining fixtures this season. It’s a game we are all very much looking forward to.’
Pompey were held to a frustrating goalless draw against Rochdale in their second game of the campaign.