The FCB supremo was delighted with the win over the Primera Division leaders but has urged his team to remain humble
Jupp Heynckes' men beat the Catalans 3-0 at Camp Nou on Wednesday to make it 7-0 on aggregate and Rummenigge was over the moon with his side's performance in the semi-finals.
"We've had two wonderful games against Barcelona, it went perfectly, but we won't turn arrogant now," Rummenigge told the official Bayern website.
"I'm almost having to pinch myself. We've won 3-0 here against the best team in the world and we won 4-0 at home. That's unbelievably good.
"I relaxed after we took the lead. I knew it meant they needed six goals and I suspected that wouldn't be possible today.
"We've achieved something that’s very tough, making the final for the third time in four years. Now we want to lift the trophy. We’ll be confident when we go to London and I believe we have a good chance of pulling it off."
Bayern will take on Borussia Dortmund in the final at Wembley on May 25 for the opportunity to be crowned European champions.