Tottenham beat Leicester 2-0 at the King Power Stadium to book their place in the fourth round of the FA Cup, with both Son and Chadli getting on the scoresheet.
Spurs looked the dominant force throughout most of the contest, despite naming a number of fringe players in their team.
And Pochettino said: "Players like Son and [Nacer] Chadli, I am really happy for them, because they got the goals but they also play so well. So yes, it is a good moment."
Son and Chadli have both been given rotational roles throughout the season so far by Pochettino.
The pair have had their chances in Spurs’ first team, but competition for places in the three spots behind the striker is fierce.
With both Christian Eriksen and Dele Alli seemingly permanent fixtures in Pochettino’s first team, it leaves one spot up for grabs - and Erik Lamela has been the most often used option in that position.
Son and Chadli will hope that their performances last night can help them receive more regular starting action in the coming weeks, though.
Tottenham will now play Colchester United in the fourth round of the FA Cup, giving them a good chance of progressing even further in the competition.