Frédéric Guilbert gave the visitors a deserved lead in a first half which Villa were the better side.
But the Villans got deeper and deeper in the second period and had stand-in goalkeeper Orjan Nyland to thank on more than one occsion for keeping the Foxes at bay.
And Kelechi Iheanacho came off the bench to finish brilliantly and level the scores for Leicester, a goal which Smith described as “farcical”.
Smith told Sky Sports: “It should be a good second leg, all square and a boisterous crowd, a full house.
“It wasn’t the performance I wanted, Leicester were the better team but we defended well at times. We have to be honest, they created chances as well. We were loose on the ball tonight, we’ve got to do better.
“I’m certainly content with a draw, just not the performance. We gave away a farcical goal. Ezri Konsa has got brain dazzled. A disappointing goal but it sums up some of our performance on the night. We did get in a lot of tackles and blocks.”