Apart from two assists in the 2-0 Group D victory against co-hosts Ukraine, Benzema has been a disappointment and was ineffective in Tuesday's 2-0 defeat by already eliminated Sweden as a below-par France reached the quarter-finals as group runners-up behind England.
They will face world and European champions Spain in the last eight in Donetsk on Saturday.
Coach Laurent Blanc must have had high hopes that Benzema would reproduce the form he showed during a fine season with Spanish champions Real Madrid, when he netted 21 league goals, seven in the Champions League and three in the King's Cup.
Tuesday's game was a case in point as Benzema made several probing runs at the bank of yellow Swedish shirts in front of him but either failed to test goalkeeper Andreas Isaksson, missed the target or had his attempts blocked.
Asked about Benzema, Blanc told a news conference: "Like all goalscorers he needs to score goals.
"He wants to, he might be frustrated because he can't find the back of net.
"He tried a lot and could have scored but did not, like the other players. I hope he gets off the mark in the quarter-final against Spain."
Benzema was left out of France's 2010 World Cup squad at a time when he was struggling to settle at Real following a high-profile move from Olympique Lyon in 2009.
However, Mourinho's cat comparison appeared to sting him into life and he slimmed down and sharpened up to move ahead of Argentina's Gonzalo Higuain in the pecking order for the centre forward position.
Perhaps the pressure of a nation's expectations is proving too much for him at Euro 2012 or international defenders are just that much better than those he faces in La Liga.
