Ulster failed to make the RaboDirect PRO12 play-offs but played a blinder in Europe this season, beating Leicester Tigers and Munster en route to the final.
At Twickenham last weekend they came up against a Leinster side in their pomp and succumbed 42-14 yet South-African Muller believes the experience will motivate the team for next season.
"At the end of the day they deserved to win that cup and it showed that we've still got a road to go," Muller told the Belfast Telegraph.
"We had a really good talk on the field and in the changing room afterwards.
"Yes 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 in our squad last Saturday was the first time and probably for 85 per cent of their squad that was the second or third time they'd been in that (Heineken Cup final) situation."
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