Benzema, who had been exiled from the France squad from 2015 until his return just prior to this summer's European Championship, managed to find the back of the net in the fifth game after his return, having played in two warm-up friendlies and two group-stage matches prior to the Portugal clash.
"There was a lot of pressure around me and I know that's normal," Benzema said in his post-match interview.
"But I never gave up and I moved around a lot and looked for chances. Today it worked for me. but the most important thing is that we are in the last 16.
"I have no doubts, but I feel that the whole country is watching me and it's normal after five years without being here. I want to enjoy it with everyone."
When asked about the pressure he has felt, Benzema explained that he felt the eyes of everyone in France on him but that it has actually benefitted him on the pitch.
"Yes, I felt it, from the whole country, but I am a football player and I am a professional and I also need this pressure," he added.
"Now I'm happy to have scored and to go through to the last 16. At Real Madrid I was used to scoring, but I wanted to do it again with France."