The England international reached his century with the opening goal at Goodison Park, although he later admitted that his effort was intended as a cross.
Kane went on to add a second later in the match as he got his goalscoring tally up and running for the season, and Pochettino was among those to offer his congratulations to the prolific frontman.
"It is not important, [whether he meant to] cross or shoot - it was a goal for us," he told reporters.
"I'm happy that he has scored 100 goals for Tottenham. He deserves a lot of praise - congratulations to him. It is an unbelievable mark for him.
"I think it was a very solid performance. I think we played well, and fully deserved in the end the result and to take the three points. I'm very pleased. We have ahead a very busy period and this was a very important victory for us today."
Kane has now scored 101 goals in just 169 appearances for Spurs.