Saint-Germain have won the league title nine times, along with several domestic cups, but without succeeding in reaching European glory.
Speaking to reporters ahead of the game in Paris, Enrique said: "When a club is obsessed with something, it's not a good sign. You have to have ambition, but obsession is not helpful in this aspect of life."
"We have to wait and see how the tournament goes. Football is a great game and there can be any result."
"You can have a great game and lose, you can play badly and win. As a team, we play every trophy to win and that's our goal. We have a lot of ambition and that's essential."
Marquinhus, defender and captain of Saint-Germain, echoed the words of his coach and said: "There is no obsession with the Champions League and there is no pressure."
"We work because we compete and the club has the determination to win every trophy, including the Champions League. We know the road and it's a long road."
Saint-Germain, who are fifth in the French league with eight points from five games, have had mixed results with Luis Enrique, winning just twice in five games in the competition.
Saint-Germain lost 3-2 to Nice on Friday, but Enrique said the variation at the start of his term was normal.
The Spaniard said: "There is a lot of information to pass on as well as ideas and concepts. The team is responding great".
"The fans are amazing and the support is fantastic, even when the results are not up to expectations."
The former Barcelona coach continued: "I have gained this experience and this stage needs time. I'm calm and we're going to play good football and we're going to get good results, I'm sure of that".
The French champions will start their continental campaign against Dortmund in the most difficult group in the current tournament, which also includes Newcastle United and seven-time European champions Milan.