Benzema struck twice in Wednesday's 3-0 Group B victory at Liverpool, taking his tally in Europe's elite club competition to 40 goals in 67 appearances, a strike rate that compares with Ronaldo's 70 in 106 matches.
Ronaldo netted the opening goal at Anfield, leaving him one short of Raul's Champions League scoring record of 71 goals, and the post-match reaction and Thursday's headlines in the sports papers predictably focussed on the prolific Portugal captain.
Benzema has had his fair share of struggles since joining Real from Olympique Lyon in 2009 but appears to be blossoming under the Spanish club's Italian coach Carlo Ancelotti.
Ancelotti has gone out of his way not to put public pressure on the 26-year-old to score goals, repeatedly pointing out that his work rate and assists are crucial to the team's success.
It is something of a turnaround from the situation under Ancelotti's predecessor Jose Mourinho, who once contemptuously referred to Benzema as a 'cat' and said he needed a dog to go hunting instead.
Mourinho's fellow Portuguese Ronaldo has given strong backing to Benzema and said after Real's 5-0 win over Athletic Bilbao this month, in which the Frenchman scored twice and Ronaldo hit a hat-trick, that he was La Liga's best striker.
"I give my all whenever I'm on the field," Benzema told reporters after the Liverpool victory, which gave Real a maximum nine points from three games as they seek to become the first club to retain the European title in the Champions League era.
"It's true that in the Champions League I'm lucky enough to score goals but the other competitions are just as important," Benzema added.
"We have a lot of players to make a good team. We're in better shape than last year."
Liverpool coach Brendan Rodgers, while full of praise for Ronaldo, also noted that Real are not simply a one-man team.
"They were outstanding," he told a news conference. "They've got many players with big-game experience and they have quality right the way through the group."
Real's next outing is Saturday's La Liga 'Clasico' at home to Barcelona and they host Liverpool at the Bernabeu on Nov. 4.
(Writing by Iain Rogers, editing by Sudipto Ganguly)
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