Already without Jack Grealish through injury, Villa found themselves 2-0 down after just 23 minutes as both James Maddison and Harvey Barnes struck for the Foxes.
Bertrand Traore pulled a goal back early in the second half for the hosts but they were unable to find a leveller.
Smith admitted he had delivered harsh words to his players during half-time.
He said: “I told them I thought their big players had turned up to play and ours hadn’t.
“Jack is going to be a loss because he is an exceptional player but we still have a good enough team there to go and beat Leicester.
“From our point of view we gave two sloppy goals away and never created enough chances to look like getting back in it.
“I thought in the first-half Leicester were aggressive in their press and crisper on the ball. Sometimes it doesn’t matter whether you are playing in League Two or the Premier League, you have to earn the right to play.”
Despite seeing more of the ball in the second half, Villa struggled to seriously test visiting goalkeeper Kasper Schmeichel.
Defeat left them sitting eighth in the table and dealt a blow to their hopes of qualifying for Europe.
“It wasn’t until we started putting the ball in behind them and got the game stretched we started to cause them problems,” added Smith.
“We got our rewards with a good goal. But it was a long way back after that first-half performance.
“You have to credit Leicester. I thought they were very good in the first-half and we weren’t.
“In the second half we showed more of what we are about. It wasn’t a half with loads of quality, I must admit. But at least we went and played in their half and asked them a few questions.”