Ben Davies gave the spot-kick away with a clumsy challenge on Konrad Laimer in the 56th minute and it leaves the Premier League top-four hopefuls with a deficit to wipe out in the second leg, but first they must focus on Saturday's trip to Chelsea.
"We are speaking about a very difficult situation and if I could, if I could, I would move immediately to the first of July," Mourinho said.
"And the first of July with Harry Kane, with (Moussa) Sissoko, with Son, with (Steven) Bergwijn, with Lucas (Moura), with (Erik) Lamela. I would love to be on the first of July, but I am not.
"We are the 19th (of February), so we have to fight until the end. I feel really proud of the boys. I arrived here 12 points behind the fourth (team). We are one point behind the fourth and we are going to fight.
"But as I was saying in some television (interviews), the Chelsea players were watching this game on TV, with nice sparkling water, with lemons and biscuits, enjoying the game and we play Saturday at 12 o'clock.
"Thank you so much for the choice. We cannot even sleep well until 10.30 or 11. We have to wake up at 7.30 for the game."
Mourinho compared Tottenham's current situation to Liverpool losing Sadio Mane, Roberto Firmino and Mo Salah and Barcelona, if they were without the services of Lionel Messi, Luis Suarez and Antoine Griezmann.
RB Leipzig dominated from the off and only two fine saves by Hugo Lloris ensured it was goalless at the break.
He was beaten by Werner from the spot but ensured Spurs were still alive in the tie with an excellent stop to deny Patrik Schick in the second period.
Tottenham did have their moments, with Bergwijn and the impressive Giovani Lo Celso testing Peter Gulacsi before Moura headed over late on.
In spite of the club's injury problems and lack of attackers, their head coach insists all is not lost.
"The result, 1-0 is 1-0, it's not 10-0. The result is open," Mourinho insisted.
"It's as simple as that. We wouldn't be the first team to lose 1-0 at home and then win the tie away. So why shouldn't we believe?"
Julian Nagelsmann was delighted with his young players and the mature performance they produced in front of more than 60,000 spectators.
He added: "I think it was a bit tricky in the end because we didn't score the second goal.
"In the game over the 90 minutes, apart from one chance from Bergwijn, I think we controlled the game, with a lot of good possession and played a mature way in the first half.
"Young teams often become impatient and think you have to score an early goal, but they weren't like that and they defended well against Tottenham's counter-attacking game."