Munster have reached the European Cup semi-finals four years on the bounce but a 24-16 loss to reigning champions Toulon at the weekend made it four straight exits at that stage.
The Irish outfit have won the RaboDirect PRO12 twice in the last five seasons - most recently beating Leinster in the 2011 final - but the top prize in European rugby has evaded them since 2008.
Rob Penney's side now switch their attentions to the league - they visit Edinburgh on Saturday looking to confirm a playoff spot - but winger Zebo conceded Sunday's defeat will hurt for some time.
"We've been here before and we can't keep doing this to ourselves every year. We want to be competing for silverware and semi-finals aren't good enough at Munster," he said.
"We will have to take a long, hard look at ourselves when we get home. It's going to have to come from within us.
"We had chances to win last year and didn't take them and it is the same this year. We need to make sure we have a fighting chance next year."
Zebo grabbed the only try in France but 21 points from Jonny Wilkinson's boot ensured the hosts pulled through on the day.
And Munster head coach Penney was left to lament an error-strewn performance that undid a potential upset for the Munstermen.
"We just couldn't control possession well enough and we made too many errors. We were thinking we were finishing over the top of them, but it just wasn't to be," said Penney
"We'll look over this game and it will be a bit ugly to watch - we were our own worst enemies today which is really unfortunate. The guys tried hard but we just weren't clinical enough."
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