Departing coach Rob Penney was unable to seal the chance of a fairytale ending after Munster were beaten 24-16 in Marseille by reigning champions Toulon.
That defeat follows semi-final exits to Clermont last season, Biarritz the year before and Leinster in 2009.
And for Zebo it is not enough to be reaching the last four of major competitions - the winger wanting his side make that next step and compete for the biggest prizes around.
"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," said Zebo.
"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."
"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."