Watkins joined from Brentford earlier this week in a club-record deal that will see Villa pay the Championship club an initial £28million.
The size of the fee raised eyebrows in some quarters, but Smith believes it is the going rate for a player who scored 26 goals in the second tier last term.
That is the same number of goals Chelsea striker Tammy Abraham netted while on loan at Villa in the Championship during the 2018/19 campaign.
Smith said: “They don’t come cheap, these type of players. Tammy Abraham did it for us the season before and if you were to try to buy him now would cost a hell of a lot of money.
“Mitrovic scored a lot of goals on loan for Fulham when they got promoted and cost a lot of money. We expected Ollie to cost and he has done. But we feel there is a lot more potential in him and that he will grow as a player and a person. He can do that at Aston Villa, that is for sure.
“It’s a tough ask, (stepping up to) one of the top leagues in the world. But I have no doubts he will relish the challenge which has been put in front of him. He has risen to every challenge so far and I have no doubts he will rise to this one.”
Watkins quickly emerged as one of Villa’s top targets following Brentford’s defeat in the Championship play-off final. He became their second signing of the transfer window, following the £16m signing of Matty Cash from Nottingham Forest.
“I know there has been frustration from supporters wanting to get players in quicker but these things take time and good things come to those who wait,” said Smith.
“I have obviously signed Ollie before and worked with him (at Brentford). I know the type of lad he is, but also the type of person he is. He will want to keep improving. We saw he had an outstanding season in the Championship last year.
“He is a team player, first and foremost, which might surprise people considering he has scored 26 goals last season. Brentford had a fantastic season and a lot of that was down to the willing running of Ollie up front.
“His finishing is exceptional and he has got better and better. He is a player who will score all kinds of goals and was my No.1 priority.”