An early mistake from Benoit Badiashile helped Callum Wilson put Newcastle into an early lead and it stayed 1-0 to the Magpies throughout the majority of the contest at Stamford Bridge.
However, an error from Kieran Trippier enabled Mykhaylo Mudryk to calmly slot home inside the penalty in added-on time, forcing a penalty shootout.
In sharp contrast to Trippier and Matt Ritchie missing their spot kicks, Chelsea produced four ruthless efforts, debutant Christopher Nkunku among those to score from 12 yards to seal a 4-2 win.
After the match, Chelsea spent time celebrating on the pitch and with their supporters, the players involved being joined by many of those who were unavailable.
Speaking to reporters at a press conference, as quoted by football.london, Pochettino referenced this, feeling that it was an important experience for his squad to experience having reached the last four.
The Argentine said: "I think these type of games are important, the way we can achieve the way to go through to the semi-final. Always it is so important. Like it is important when you don't play well, games like Everton and Newcastle away from home, to realise in which area we need to improve.
"Both are really important and to really feel for this group, in the way we want to evolve and develop the ideas. So pleased because I think when you see the whole squad, players that weren't involved in the game, players that were injured but they wanted to share the happiness in the middle of the pitch.
"I think it looks like we are a healthy group of players that only need time and our responsibility is to guide them to really improve every day.
"With time I think we are going to create a very good team that can compete and increase the competition and can be in the place that Chelsea should be."
Chelsea will now await the draw for the semi-finals on Wednesday night, where they will be drawn against Middlesbrough, Fulham or one of Liverpool or West Ham United.