The Arsenal star was unavailable to Dragons boss Chris Coleman as he was suspended due to an accumulation of yellow cards during the Euros. Wales lost the tie 2-0 to the eventual tournament winners.
"There is still a tiny little part of you that thinks maybe we could have got to the final or maybe won it," said Wales captain Williams.
"I don't think it is a silly thing to say we could have won it – if we had played a bit better in the semi or had Aaron Ramsey been there.
"He would have made a big difference. All these ifs and buts."