Harry Kane and Ndombele had opened a two-goal lead but strikes from Leander Dendoncker and Daniel Podence, who profited from Ndombele's concentration lapse, sent the third-round tie to penalties.
Dendoncker then saw his effort saved by Pierluigi Gollini, with both Conor Coady and Ruben Neves missing as well to hand Spurs a place in the fourth round for the eighth time in the last 10 seasons.
Despite the shoot-out win, Nuno focused on Ndombele as he insisted the France midfielder needs time to regain confidence and settle in.
"Let's try to avoid as much as we can individual analysis," Nuno responded to reporters post-match when asked about the mistake for Wolves' second goal.
"We will do it and we will do it amongst ourselves and I think we have to be patient with Tanguy because of all that happened in pre-season and this is his third game and already we've had however many games we've played so far.
"So let's be patient with all our players and patient with the time that they need to get to the level that I truly believe their talent can allow."
Kane, who has still not scored in the Premier League this term, was also on target and Nuno used his captain as another example for why patience is required with his players.
"In terms of the squad and in terms of the preparation of the squad we have players who have 65, 70 [training] sessions and we have players who have 15 sessions," he continued.
"Until we can balance everything, I think that will be the moment the players improve and get better. Harry [Kane] did a very good game, I think he has much more to give and it's about the team improving and growing together."