O'Shea scored a late equaliser on his 100th international appearance in Gelsenkirchen on Tuesday as Ireland earned a point to maintain their unbeaten start in Group D.
The result has seen Ireland remain in second place in the standings, with Poland leading the way on goal difference after three games.
"It's brilliant for him," Quinn told Sky Sports News. "He's taken the mantle of the leader of that Ireland side and he's bought in to everything Martin O'Neill brought to the team. He leads by example and I am thrilled for him."
Ireland continue their qualifying campaign on November 14 when they travel to Scotland.