The Real Madrid striker set up both goals at the Donbass Arena on Friday, and told of his delight at contributing to a solid victory for Laurent Blanc's men
The Real Madrid man became the first French player to produce two assists in a single European Championship game in 28 years, setting up Jeremy Menez and Yohan Cabaye within three minutes of each other in a rain-interrupted tie in Donetsk.
The 24-year-old insisted that while the victory would go far to build confidence within the French camp, it left Laurent Blanc's men with work to do to secure a quarter-final berth.
"It was important to win. We are all pleased with the outcome of tonight [Friday]. We did not concede a goal, and we took all three points." Benzema was quoted as saying by RMC Sport.
"It's been a while since we had not won a [game in the] European Championship or World Cup. We're all very proud of this result.
"We all had a good game. We played together, we had chances. [Ukraine] were very tired. We had the mastery of the ball. We must continue like this.
"[Assisting a goal] is not totally the same [as scoring]. But it's nice. I like to participate. In addition, it is known that Menez is my buddy. I'm happy for him and also for Yohan.
"We needed this victory, which was very important. There is always a lot of happiness when you come back to the hotel. You know you'll sleep well because you have taken four points from two matches."
Asked whether the win left Les Bleus in a strong position to qualify for the last eight, the striker remained coy about the team's chances.
"I do not know. It's good; we have our destiny in our hands. We must not lose. We must continue to play like we did," he added.
France conclude their Group D campaign against eliminated Sweden on Tuesday. Kick-off at the Olympic Stadium in Kiev is at 20:45CET.