The 26-year-old midfielder has joined Premier League rivals Stoke City for £13m after the Swans' £8m bid was rejected in June.
Saunders added that Allen had been praised by ex-Manchester United boss Sir Alex Ferguson for his performance at Euro 2016.
"I was speaking to Sir Alex Ferguson and he said, 'What about Joe Allen's performances in the Euros? What a player he is'.
"It is a disaster for Swansea. Mark Hughes knows him but I am disappointed as a Swansea fan. He is a great player."
Allen was named in the team of the tournament after helping Wales to the semi-finals in their first major finals appearance in 58 years.