Pochettino's Spurs were thankful for a brace from Son Heung-min, whose goals ensured that Tottenham enjoyed their best start in the top flight of English football for 51 years.
"We fully deserved the result - the most important thing is the victory. Son was fantastic but it was a collective effort," said Pochettino, according to BBC Sport.
"The first half was great and we should have scored more than two. We need to learn to be more aggressive and clinical."
Victory at the Riverside has seen Spurs climb into second place in the league standings.