Romelu Lukaku’s brace and a Mateo Kovacic strike earned the hosts victory but it was Villa who were the better team for long spells.
Smith’s team had more shots on goal and on target but could find no way through with Ollie Watkins denied on several occasions.
The boss said: “I thought the 3-0 scoreline was unjust. But football is about moments and we didn’t take our moments today.
“I feel with the squad we have now we don’t have to come to Chelsea and play with a block.
“I feel with the quality of our squad and their athleticism we can ask questions. I thought we did that in the second half.
“Unfortunately, the second goal was a bad mistake and gave us a mountain to climb. There are certainly positives to take. The squad is getting better. There is an awful lot of belief in this group.”
Lukaku’s 15th minute opener had Chelsea ahead at the break and Villa fell further behind when Kovacic pounced on a poor backpass by Tyrone Mings to finish.
Though the visitors kept pushing, Lukaku’s stoppage time effort ended any chance of a comeback.
Smith added: “The second goal changes the game. That was the killer, we made a big mistake and they capitalised and it took the wind out of our sails.
"Our players never gave in and I'm pleased with the depth of the squad. We felt we could pressure them high and play high in their half.
"That's why they paid £94m [for Romelu Lukaku], he can put it in the top bin, as he did. I'm disappointed at 3-0 and anyone who has not seen it will think it was comfortable for them but it was not a bit comfortable."