The Devon club were denied a second major final appearance this season when Aviva Premiership rivals Gloucester edged them out 30-19 in a hard-fought semi-final encounter.
However, the Australian international - who is to leave the Chiefs at the end of the current campaign following three highly successful seasons at Sandy Park - was in defiant mood when addressing the media following the game.
"We're disappointed - as you would be after losing a semi-final - but there is still so much to go after in this season and still so much to achieve," said the 31-year-old. "I'm ambitious to get it and so are the boys, Rob and Tony.
"The whole set-up at the club wants more from this year and it all starts again this week, it starts again on Tuesday when we'll look to get right back on it again."
Having advanced to the latter stages of both the LV= Cup and Europe this term, it's the final rounds of the Premiership that will now dominate the thoughts of Mumm and his fellow Chiefs over the remaining few weeks of the season.
With Wasps at the Ricoh Arena first up this Sunday, the Chiefs - who occupy the last of the four play-off berths - know this really is the business end of the season and the time for them to deliver their biggest results.
"We're a team that often responds to disappointments quite well," said Mumm. "After this latest result, we're going to have to. We've got a huge game coming up at Wasps and we know it will be a big challenge going up there.
"Yes, this result will hurt now and probably on the bus journey home, but by the time we report back in for training this week, it'll be time to refocus our thoughts again and look to move on once more."
Certainly Mumm knows the character of the Chiefs will determine that there is a response of sorts against Wasps and he says the club must look to channel their disappointment into a big, positive display in the Midlands.
"We lost brave and that's important, particularly going forward," added Mumm. "We lost some key moments and the 50-50 moments seemed to go Gloucester's way. Also they were a team that worked very hard for that win, so you have to give them credit for that.
"They were desperate for that win and as a result they got the win in the end. That said, we never gave in and we were fighting right until the death. We gave it a real good go and as players and coaches, that's all you can ever ask for."