The Real Madrid striker was brought back for Euro 2020 by coach Didier Deschamps after a five-and-a-half year exile from international football over his alleged role in a blackmail plot.
Benzema failed to score in his first four matches since returning for France, who won the 2018 World Cup without him.
But he netted a first-half penalty in the final Group F game against Portugal before slotting in a second to end his long wait.
“A lot of joy, a lot of pride,” he said to BeIN Sports.
“I think everyone was waiting for it. There was a little pressure on me from all over the country but I’m a footballer, a professional — I need that pressure.”
A 2-2 draw, which also saw Cristiano Ronaldo score twice to equal the all-time international goalscoring record, sent France through as group winners.
Deschamps’ men will face Switzerland in the last 16 on Monday in Bucharest.
“He (Benzema) was looking for that. He hasn’t lost his confidence, or mine,” Deschamps told TF1.
“We will recover well and then we’ll prepare for that (Switzerland game) as well as possible.”
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