The England midfielder was signed on loan from Chelsea last week.
And after Barkley scored in Sunday's 7-2 win over Liverpool, Smith was delighted with his impact.
"He does. We tweaked our system and had two holders in Douglas Luiz and John McGinn and freed up Ross as a 10 and tried to keep them down one side.
"We wanted to make sure we were good behind the ball and we executed the gameplan expertly.
"You don't very often get a performance and result like we have tonight against the champions. The biggest regret is that there are no supporters because this place would be rocking."