In what amounted to a routine win, fifth placed Tottenham emerged with a 2-0 score line in Wales, which helped them get back into contention for a top four finish.
Wanyama came on in the game during the 59th minute, replacing centre-back Davinson Sanchez.
"It's important he's back after a lot of months. It gives us more options to play and he was very important for us last season," said Pochettino.
"Sanchez was in a difficult situation. The fans started to put pressure on the referee and the clever thing was to take him off and take away any problem."