Spurs come to Amsterdam needing a special performance if they are to reach the final of this competition for the first time in their history after a Donny van de Beek away goal condemned them to a 1-0 defeat in London last week.
However, Pochettino's team have already made history for the club by getting this far -- they last reached the semi-finals of the European Cup in 1962 before being beaten by Eusebio's Benfica.
Now they are dreaming of a first European final since Keith Burkinshaw's team beat Anderlecht on penalties to lift the UEFA Cup in 1984, before any of those set to feature on Wednesday were born.
"We are living a dream. Five years ago when we arrived it was to reduce the gap to the top four, and then to have the possibility to play in the Champions League," Pochettino said at the Johan Cruyff Arena on Tuesday.
"I think nobody would believe we would be playing in the Champions League three seasons in a row and competing at this stage."
- Stumbling -
However, his side are stumbling badly towards the finish line with a depleted squad, set to finish in the top four in the Premier League mainly thanks to the failings of the teams below them.
Harry Kane is out, and Tottenham have been beaten five times in their last six games in all, nine times in their last 10 matches away from home.
The exception in that run came on their last trip to the continent, however, against Borussia Dortmund in the last 16, and now they arrive in Amsterdam with Son available after sitting out the first leg due to suspension.
Jan Vertonghen, who began his professional career in Amsterdam before joining Tottenham in 2012, is in line to return too after coming off with a head knock in the first leg.
"You wouldn't believe at the start of the season that Tottenham would be in the last week of the season with the possibility of being in the final of the Champions League and to be in the top four," Pochettino insisted. "Both are real, but this is not the moment to talk."
Spurs' status as one of the Premier League's top six clubs gives them a considerable financial advantage over Ajax, but they cannot match their opponents -- four times European champions -- when it comes to history.
The club of Cruyff and so many other great names are in sight of a first Champions League final since 1996 and remain in with a chance of a treble, something they last did in 1972 when the man after whom their stadium is now named was starring on the pitch.
- Treble dream -
Erik ten Hag's team secured the first leg at the weekend when they beat Willem II 4-0 in the Dutch Cup final, and they are top of the league in the Netherlands with two matches left.
They are aiming to carry on an incredible European run that began in the second qualifying round against Sturm Graz on July 25.
"You don't expect at the beginning of the season to be in this position. I am very proud and happy to be here during this special period," said Daley Blind, almost echoing Pochettino's own remarks.
Blind, who returned to the club from Manchester United just before the campaign began, admitted that celebrations after the Cup final were "a bit timid" due to the proximity to this match.
Ajax are now hoping they don't live to regret not scoring more than once in London.
"Our defensive organisation was excellent," pointed out Ten Hag. "In the final third we didn't play all that well but the players' mindset was to defend our 1-0 lead."
If they can finish the job on Wednesday, they will be the ones to advance to the final in Madrid on June 1.