Thomas Tuchel praised Paris Saint-Germain's "heart" after their underwhelming 1-0 Champions League win over RB Leipzig and refused to apologise for winning ugly.

Last season's beaten finalists were badly out of sorts against their Bundesliga opponents on Tuesday, with Neymar's decisive 11th-minute penalty just one of three shots on target they mustered.

The result means PSG leapfrog Leipzig into second place in Group H courtesy of a better goal difference with two games remaining. 

Under pressure head coach Tuchel concedes his side were lucky to claim all three points at Parc des Princes, but refused to say sorry for winning by any means necessary. 

"We lacked luck in Leipzig [they lost 2-1 in the reverse fixture three weeks ago] and tonight we had some luck," he told a media conference. "We played with a lot of solidarity and defended with a lot of heart. 

"Always together. That's why we won. I'm not going to apologise for that. The match demanded that we defend deep and we just did what the game demanded of us.

"Tonight it wasn't possible to get out of pressure with the ball and we have to accept that. I accept it.

"We want to attack. We've done that before. But sometimes it's just not possible."

The Ligue 1 champions ended the first half with just 37.2 per cent possession, their lowest total at half-time in a Champions League game since facing Bayern Munich in September 2017.

It did not get much better after the interval, with Leipzig finishing the game having enjoyed 62 per cent possession and taking 15 shots to PSG's eight. 

Tuchel blamed his side's lacklustre performance on injuries and fatigue after a busy start to the season, but he is targeting an improved performance against group leaders Manchester United next week. 

"We've played 11 league games and four Champions League games, and we've had around 100 injuries during that time," he added. "I saw that we average seven injured players per game. 

"We have another game in Manchester next week. I hope we're able to recover but we have another game on Saturday [against Bordeaux in Ligue 1].

"Marco Verratti played today practically without having trained. The same for Neymar. That's the reality. Maybe you think it's always excuses. 

"The most difficult thing was to find 11 players who could make a physical impact. We'll prepare a plan for Manchester. If the players feel better, we'll play a better match. If we have to defend deep again, then we'll do that."