The French giants struck twice in the final minutes against Atalanta to book a place in the semi-finals, half a century on from when they were founded.
Tuchel - who spent the match on crutches after suffering a sports injury - said: "Imagine what I would have done [with my celebration] if I had two legs! Maybe today would be the day you would see me sprint for 40 metres. But it's the club's birthday today, exactly 50 years, so we will not forget this birthday."
PSG reached the last four of the competition for the first time in 25 years and Tuchel praised his side for overcoming a lack of match preparation to progress in Lisbon.
The German coach said: "It was very difficult to prepare the team.
"There was no rhythm because there were no games, but I could feel in the last days that the determination, enthusiasm and effort of the group, the quality of the training and the mix between love and hard work, was exceptional.
"For me, it was a deserved win, but if you score so late it was also luck - but I'm the first one to admit you need luck."
Tuchel also hailed the victory as a "big step", with the Parisians suffering agonising defeats to Barcelona and Manchester United in recent European campaigns.
The 46-year-old coach said: "We are very happy to be part of it [this moment in the club's history]. People from outside don't realise how hard it is to reach all these goals, even if it seems easy with a good team and a big squad. But it's a big effort and it's a very big step for all of us."