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It was a disappointing end to the season for the Belfast-based province but the quality of Leinster's performance prompted Muller to admit that even their very best showing wouldn't have been enough to stop the champions.
"They played the perfect game of rugby and we were below par," Muller told the Belfast Telegraph.
"You want to blame everything and everyone but I think, looking back now, even at our best, I don't think our best was going to be good enough against that Leinster side.
"I thought they were just in a different league. If you really have a look at the game and count the number of mistakes they made, it's not going to be a lot.
"At the end of the day, they deserved to win that cup and it showed that we've still got a road to go."
But rather than remain downbeat about the Twickenham experience, Muller will be taking plenty of positives into next season as Ulster look to go one step further in Europe's greatest club competition.
The magnitude of a first Heineken Cup Final appearance in 13 years shouldn't be underestimated, especially when you consider that the likes of ASM Clermont Auvergne, Leicester Tigers and Munster were beaten en route to London.
And while the pain of defeat will linger a little longer, the South African second row insists Ulster will be a stronger side for the experience.
"We had a really good talk on the field and in the changing room afterwards," added Muller.
"This wasn't the way we wanted to end the season but you could just see the hunger and the passion in the guys. Personally, this will inspire me to be better and stronger for next season.
"For a lot of the guys, we've tasted a little bit of success this season but I think they want the 'full metal jacket'.
"They want the whole thing and I truly believe that everyone in this squad feels that way and that they'll come back with a new hunger and they'll want to be the top side not the second.
"For every single one of our squad last Saturday was the first time and probably for 85% of their squad that was the second or third time they'd been in that situation.
"They've been in these situations and learned from them and now we have to learn from this as well just as we did against Northampton the previous season.
"It's an easy thing to say that you've got to learn but I think the day that you stop learning is the day that you stop playing rugby."
