The on-loan Chelsea midfielder was at fault of two of City's six goals on the day.
But Smith insisted, "Danny Drinkwater will make us a better team. I thought he started the game well, got on the ball and played some decent passes.
"He's made a mistake for their second goal, but I think there was a mistake in trying to run the ball out before that as well.
"He got 75 minutes of match time today, which he needed. He's come in and looked good in training and he certainly wasn't the reason we've been beaten 6-1 today."