The Bavarians, who lost the 2010 final to Inter Milan and the 2012 edition in dramatic fashion in Munich to Chelsea on penalties, take on Bundesliga rivals Dortmund in the first all-German final of the competition at London's Wembley Stadium on May 25.
Defeat to bitter rivals Dortmund, who won the league in 2011 and 2012, was not an option for this year's Bundesliga champions, Mueller said.
"It is time we won this trophy because if we lose it will be three times and then you get sort of stuck with a 'loser' tag which is something you do not want," said offensive midfielder Mueller, preparing for his third Champions League final at the age of 23.
"I am a bit younger (than some of the other players) and hopefully I still have a few years of international action left in me but we really have to win it this time."
Mueller said he relished the clash with their German opponents.
"There is a lot of spice in this game and I like spice and I like that we play against Dortmund because there is even more passion in there," he said.
For coach Jupp Heynckes, who will make way for former Barcelona coach Pep Guardiola at the season's end, there are no major surprises when it comes to Dortmund.
"I think both teams know each other very well," Heynckes said. "There are no secrets and a final is an open game, a game where chances are roughly equal but in the end it is decided by the players on the pitch.
"I think there are no tactical surprises but every coach has a concept, a plan and it is up to players to interpret that on the pitch. My team have been doing that outstandingly all season and especially against Juventus and Barcelona in the previous rounds."
Bayern beat Italy's Juventus in the quarter-finals and then crushed Barcelona 7-0 on aggregate to book their final spot.
Heynckes said Bayern's second consecutive final appearance was down to continuity and a strong squad.
"I told my players earlier that we played a great season last season (despite three second-place finishes)," said the 68-year-old. "We had 14-15 players who played throughout. This season it is 20-21 players, almost all equally good.
"We set the foundation for such a season in the close season. There were very good transfers, we improved our fitness, we modified things and our defensive game and you can see that from the few goals we have conceded it was not perfect but worked very well."
Bayern let in 15 goals in 33 league matches this season and are set for a Bundesliga record with one game left in the campaign.
Heynckes also praised his players' mental strength after last season's losing final in Munich.
"To come back after such a bitter disappointment, being the better team over 90 minutes and then lose, to come back and play such a season requires special people and my players are exactly that."
He had special praise for playmaker Bastian Schweinsteiger, who missed a crucial penalty in the shoot-out against Chelsea.
"He is a strategist, he determines the pace of our game. Obviously he was disappointed, he had to swallow it and digest it. But he has been decisive for us in the last months and for me he is at the moment the best midfielder in the world.
"He is mentally and physically strong and, like many of his generation, has the hunger to win the Champions League."
Schweinsteiger said landing a first major international trophy would be great but missing out on it would not be the end of the world.
"Every win is important. It is not every day that you reach the final and certainly not three times in four years. This has motivated us more to do it this time," Schweinsteiger said.
"But it is not that I will live longer if we win it. If we win we will be happy; if not there will be reasons why not and we will try again next year."
- Sports & Recreation
- Jupp Heynckes