The Strictly judge said: "That's terribly sad because she was terrific. Could have made it all the way to the final, I thought she was very, very strong."
When Hammond suggested Abbington could perhaps come back to the show for another year's competition, Du Beke agreed that "maybe she could come back".
After her exit was announced, Abbington said in a statement posted to Instagram that "it is with deepest regret" that she had to leave the show "for personal reasons".
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She continued: "It was an absolute joy working with my fellow contestants, they are a beautiful, hardworking and talented group of people who I love and who I will miss seeing every Friday and Saturday and competing alongside.
"I want to thank the incredible production team and everyone on Strictly who looked after me and who are so kind and caring. It's a wonderful bunch of people and I'll miss all of them."
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Meanwhile, her partner Giovanni Pernice said in an Instagram post that he was "so sad we can't continue", but also that he was "proud of what we achieved and I am sending you so much love".
Abbington and Pernice scored well across their dances, getting between 29 and 32 points from the judges across all four weeks.
Strictly Come Dancing continues on Saturday 28th October at 6:40pm. The results show will air on Sunday 29th October at 7:20pm on BBC One and BBC iPlayer.
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