Defender Jan Vertonghen opened the scoring with a header that needed goal-line technology to be confirmed, before England international Dele Alli restored the visitors' lead following Joselu's equaliser for the Magpies.
All three goals came inside the first 20 minutes at St James' Park, and despite late pressure from Rafael Benitez's side - including two shots that hit the frame of the goal - Spurs held on for the three points.
"I am so proud of the performance in the circumstances," Pochettino told Sky Sports News. "Newcastle are a very good team and they had some chances to score more than one, but sometimes in football you need some luck as well as effort.
"With all of the circumstances, we prepared for the game with a lot of players that only started training on Monday.
"We can do better, of course, and be more consistent but it was a massive challenge to connect everything and prepare in the few days we had. I am not going to complain and we have to learn to be clever. It is a massive challenge to work together again."
Tottenham's victory over Newcastle was the second in succession on the opening day of a season.