Villa were beaten 3-0 at Stamford Bridge but the boss believes his players will have taken belief from a commendable display against the Champions League winners.
Smith said: “For me, Saturday was our best performance this season. There are reasons for that. For me the health of the squad these first three games has been difficult.
“I think it was a big step forward in terms of our performance levels. The way we took the game to Chelsea in that first half will give the lads a lot of belief in what we are doing.”
Villa were well on top for much of the first-half but were unable to capitalise and trailed at the break to Romelu Lukaku’s 15th minute opener.
A mistake by Tyrone Mings then allowed Mateo Kovacic to double the home side’s advantage early in the second period, with Lukaku bagging his second in stoppage time.
Villa now host Everton on Saturday and Smith said: “I feel we can grow from Saturday’s performance.
“Obviously we are disappointed with the result and feel it was a little bit unjust.
“Our performance levels are certainly getting there and I think a couple of teams will certainly respect us a bit more than perhaps they did before.”
Smith pointed to Mings’ error, when he underhit a pass intended for goalkeeper Jed Steer, as the key moment of the match.
He said: “Tyrone held his hand up in the dressing room. That was a moment which changed the game a little bit.
“It took the wind out of our sails and we had to try and change things from the bench and go away from the gameplan.
“At 1-0 we always felt we were in it. At 2-0 they made the pitch big and it made it difficult.”