"We are aware that the club's decision to find a new format to recreate and preserve the messages on the heritage tiles has caused distress to some fans and confusion for others. We are very sorry for this," Barber wrote in a letter to fans.
"We are fully aware that many tiles represent significant sentimental and emotional moments and connections in people's lives, hence our desire to protect and preserve the messages.
"In looking at all new options, we have listened very carefully to the heartfelt feedback we have received in the past few days and we will not merge the heritage messages with the new 125 wall as originally proposed."
Brighton aim to have the new installation in place during the 2026-27 season, and have said that all current messages on tiles will be transferred for free.
Barber said that nothing will happen to the existing wall until the end of the season.