Tomorrow’s Carabao Cup third round tie at Chelsea is the first of three straight away matches against members of the top flight’s established big six, with Villa visiting Manchester United on Saturday and Tottenham a week Sunday.
Smith believes his squad is now strong enough to go toe-to-toe with the best teams in the country.
He said: “These are the games we want. We want to challenge ourselves and believe we can.
“There are no easy games at this level. We have just played Chelsea and Everton and are now playing Chelsea, Manchester United and Tottenham.
“The win over Everton will have given everyone confidence and belief moving forward.”