The Welsh region's heartbreaking 22-20 defeat to Munster left their chances of finishing in the top four hanging by thread.
Mathematically the Ospreys can still squeeze into the play-off places but they are reliant on other teams dropping points.
"We thought we could close the game out but it was not to be," said Humphreys.
"It comes with a bit of composure. I hope we can do that in the future. We have done it in the past.
"You couldn't say we lacked character or spirit out there; the boys were fantastic but it didn't go for us at the end.
"We conceded too many penalties, more than we normally do. But some of those were down to interpretation and could have gone slightly differently.
"We're looking to build for the future and there was a lot of good."
But Humphreys is adamant that his side will give everything to the cause in the hope that they can sneak in to the knockout stages.
"Mathematically we can still do it," said Humphreys.
"We have to go to Aironi and it's a difficult place. By no means is it a given.
"But I can ensure you that we'll prepare in a professional manner and take the positives out there.
"We won't give up, while we still have a chance we have to go for it.
"We owe that to our wonderful supporters, to the board and to everyone involved with the Ospreys."
Humphreys reckons the Swansea-based region only have themselves to blame for their failure to take control of their Magners League destiny.
They had been cruising earlier in the season and looked odds on to finish in the top four thanks to a four match winning streak during the RBS 6 Nations.
But the Liberty Stadium-based side have hit a major blip and have lost three and drawn one of their last four games.
"We're reliant on other people; a few short weeks ago destiny was in our hands," added the former Wales skipper.
"But we have been the architects of our own downfall, which is disappointing. Results have put us where we are in the table."
"We're a little bit off as a team in terms of form, but in terms of character and spirit we were right on the money.
"Last year we had that killer instinct in abundance. We went through some very difficult games and managed to come out the other end."
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