The Gunners were repeatedly linked with a move for the Schalke 04 attacking midfielder, but a reported £35m bid failed to materialise.
Speaking to Sky Sports News, Smith said: "We're all left a bit disappointed that Julian Draxler never arrived.
"Was it a question of money? We'll never know, but the signing would have carried on the feel-good factor from the Mesut Ozil signing.
"There's a tough run of fixtures coming up and the fans may become disheartened."
Arsenal are currently second in the Premier League.