Swans chairman Huw Jenkins had suggested the club would match the £13m bid from Stoke, who are managed by former Wales boss Mark Hughes, but his move to the Potters was confirmed on Monday.
“I was speaking to Sir Alex Ferguson and he said, ‘What about Joe Allen’s performances in the Euros? What a player he is’,” Saunders, who won 75 caps for Wales, told BBC Radio Wales Sport.
“It is a disaster for Swansea. Mark Hughes knows him but I am disappointed as a Swansea fan. He is a great player.”
Allen’s former Swansea and Wales team-mate, ex-midfielder Owain Tudur Jones, said Swansea have “missed a trick” by not bringing Allen back to the Liberty Stadium.
“He’s certainly a player that could have added to their squad for years. He would have been a player that they would have got in his prime,” Jones told BBC Radio Wales Sport.
“Joe is a guy who could potentially have come in as a future captain.
“Stoke are a good progressive club with a manager that’s trying to do things the right way. “I would assume the only reason they would sign him is because they want to use him and use him in the middle of that park.