Great Britain's Davis Cup Finals team advanced to the quarter-finals of the 2021 tournament after a 2-1 victory over the Czech Republic.
Smith paid tribute to his players' performances after their quarter-final spot was booked, telling BBC Sport: "It's great. Today was tough. A lot of people look at the rankings but it's never like that. We've been underdogs and managed to get wins.
"The Czech team played well - very young team. Machac turned into a top 20 player overnight! I'm absolutely thrilled for these guys - to come out and play as well as they did today - I'm really proud of them."
GB have reached the Davis Cup quarters for the sixth time since 2014 and will face Germany or Serbia for a spot in the semi-finals on Tuesday.