United qualify as one of the two best runners-up while Bayern also progressed as Group D winners after the 1-1 draw.
Ferguson said: "I knew we were OK with 10 minutes to go because the Germans are never wrong with these things. They have the best information."
Ferguson claimed his biggest problem towards the end was convincing his players that a point would be sufficient. "I knew it was good enough and I had to emphasise it to the players," he said. "I think they should make announcements to the fans so they would all know."
United are through to the last eight for the third successive season and Ferguson is confident about his side's chances after they emerged unbeaten from the "Group of Death".
"At the start of the group it looked a really difficult task for us and we have achieved a lot to come through as good," he said.
"We have scored 20 goals and you can't dispute that. That is good form. Even tonight we looked like scoring goals and we have shown we have got the ability to do well."
The Bayern coach, Ottmar Hitzfeld, was pleased both sides had qualified and he feels United have improved since he led Borussia Dortmund to victory against them in the 1997 European Cup semi-final.
"This team of Manchester United has two years more experience while they have also got players like Jaap Stam and Dwight Yorke therefore it is a better team," he said.