Liverpool bounced back from that embarrassment against Barnsley to beat a team rated the best in Europe on current form.
Benitez, his job reputed to be on the line, said: "This result is good for the confidence of the team, the supporters and the club.
"I always had confidence in my players, they played well with passion and they passed the ball excellently.
"It was clearly much better than the last match - and even though Inter Milan had 10 men for a long spell, they were still formidable opponents who were organised, defended well and were always capable of scoring on the break.
"I accept that we needed this win as a team - we needed to progress in the competition. As a manager, you are always pleased with a win like this - and this is now the time to be happy."
He said: "The red card was clear. It was for two yellow cards, and the referee was right. As for the penalty, everyone could see the Inter player handling the ball.
"But you cannot change things now. It is an excellent win, made better by a clean sheet.
"I know people will say they cannot understand how we can lose to Barnsley and then beat Inter Milan. But on Saturday we changed the team, we had 10 internationals on the pitch and missed a lot of chances.
"This time we were better - we had far less chances but we scored two good goals. It gives us a great chance in the second leg, but we must be careful because Inter are a very good side and they will make it very difficult for us at the San Siro."