A Jay Rodriguez brace and Rickie Lambert's 27th-minute effort put the visitors well in control by half-time at the Cardiff City Stadium as Southampton picked up their first Premier League win in seven matches.
Pochettino felt Southampton were much the better side, adding that it was just reward for their performances in recent weeks - games in which he felt his team had been hard done by.
"I think overall we had an amazing game, we were precise in their half, we put in an amazing shift," he said.
"We fully deserved the result.
"In the previous few games we played well but the results did not come our way.
"We maintained out style and the way we want to play but the results did not come our way."
Pochettino saw defender Dejan Lovren miss the game due to illness, while the likes of Nathaniel Clyne, Guly do Prado, Victor Wanyama and Pablo Daniel Osvaldo were also absent.
Lovren, Clyne and Osvaldo could all return in time for Saturday's trip to Everton, but Pochettino was delighted with how his injury-hit team fared.
"We've been going through a tough period in terms of illness and injuries so to get that win was very important," he added.
"We were superior, we played very well and we deserved the win."
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