Although Wallabies flanker George Smith now looks likely to become the only Australian in the modern era to play the Lions in two series, Mowen pointed out that this was the only chance his generation would have of winning a series against tourists.
Having won his first cap in the 23-21 defeat in Brisbane and his second in last week's 16-15 victory in Melbourne, the loose forward is still getting used to the pace of Test rugby but is expecting another level again this weekend in Sydney.
"It will be a huge step up in intensity. When you start the series there is still a chance that if you drop a game you can recover. There is no recovering from this one," he told reporters.
"I know the Lions have spoken a lot about how it will be four years until they get to play again and some of the guys won't play in another Lions series and they want to play in a winning Lions series. This is our only Lions series.
"We get to play them once every 12 years. Some guys like Nathan Sharpe never got to play against them. We don't want our only memory of the Lions to be of losing the series to them.
"At the end of the 80th minute that's the end for us as far as out rugby careers are concerned. You only get one crack at this. I can't even think about not having the cup with us - it would be crippling."
Wallabies coach Robbie Deans always said he would be reluctant to throw inexperienced players in at the deep end in a Lions series and Mowen has repaid the New Zealander for his gamble with two fine displays at blindside flanker.
The home side edged the breakdown in the first Test, while the Lions enjoyed greater success in the second and that was something the Wallabies spoke about this week, Mowen said.
"We probably got a bit lateral in our support lines in the second Test," said.
"We weren't giving them huge windows into the breakdown but it was enough for them to make a huge difference and we certainly weren't happy with the number of times we turned the ball over.
"They have lost Sam Warburton, who was huge for them last week, but they have two very good sevens to pick from. Bit it wasn't just the sevens were doing the damage. Out wide it was (Conor) Murray on the ball or (Brian) O'Driscoll. They obviously had a huge focus on it."
Mowen captains the ACT Brumbies in Super Rugby and the way he has played and carried himself in the Lions series has already seen him marked out as potential future Australia skipper.
Such matters are looking a little too far ahead, though, for a 28-year-old resolutely focused on Saturday's match at the Olympic Stadium.
"There will be one or two opportunities in the entire 80 minutes and it will be down to the side that takes them," he said.
"We are in good shape, in really good shape actually. I feel fitter and fresher now than I did after the first Test.
"There will be no excuses for us on Saturday night we just have to make sure we pour everything into it."