PSG swept the board domestically and are into the last four of Europe's premier competition for the first time since the 1994-95 season.
The Champions League remains the ultimate goal for the Ligue 1 heavyweights and their owners, Qatar Sports Investments.
Most pundits make PSG favorites to reach the final, but Herrera says his club has already had a successful campaign.
"If we didn't win the Champions League, it wouldn't be a failure. It would be a failure for 10 teams then," he told a news conference.
"We have already done a fantastic job at the national level with four titles won this season. But it is true that Leipzig, or Lyon for example, perhaps didn't expect to be here.
"We have the quality and the ability to win the semi-final, but we have to know they will play free, without the pressure of winning the game."
Herrera believes Leipzig head into the contest without the same pressure as their opponents, a fact he says makes the Bundesliga side dangerous.
"They are a very offensive and very courageous team. They don't have the pressure of having to win the Champions League or play the final. It may be more dangerous for us," he added.
"They have a diagram with the ball, and another without. We will have to prepare well for this match because they will play more liberally, with less pressure.
"The fact that they are offensive can be a good thing for us because our attackers can build up speed, but we will also have to defend well, because they can create a lot of chances."
On Friday, Bayern Munich humiliated Barcelona 8-2 in their quarter-final tie to lay down a marker to the remaining hopefuls in a tournament that is being completed in Portugal due to the coronavirus pandemic.
Herrera was impressed by what he saw but said PSG cannot contemplate anyone else but Leipzig.
"We were all impressed with the result. It’s the first time in history that something like this has happened in the quarter-finals, but we prefer to be aware of Leipzig," he said.
"Our goal is Leipzig. The most important thing is to prepare this game against a team that played fantastically against Atletico Madrid.
"We saw a team with a lot of confidence. Leipzig impressed me too. We have to be very respectful of this team and prepare the match in the best possible way."
Herrera says PSG's variety of options can play into their favour.
"This season, we have played in several systems, with three central defenders, in 4-4-2 or in 4-3-3 as well. We have a lot of good players and possibilities," he said.
"It's not just Di Maria. Mbappe seems ready to help, Neymar too, Pablo Sarabia is reliable. He gives assists, he scores goals.
"We are very respectful towards Leipzig, but we are confident because we have a lot of players who can play and change the course of a game."