Menez marked his first start for the Rossoneri since April 2015 with a brace of goals in a 5-0 rout of third division Alessandria on Tuesday that allowed Milan to end a 13-year wait to contend the Italian Cup final.
Sinisa Mihajlovic's men will now meet the winner of the second leg of the semi-final between Inter Milan and holders Juventus, although the latter take a 3-0 first leg lead to the San Siro later on Wednesday.
The final will be held at Rome's Stadio Olimpico on May 21, and for Milan it has special significance as the winner will secure entry to the group stages of next season's Europa League.
With Juventus vying for their fifth consecutive 'scudetto' they will be expected to clinch one of three Serie A places that offer entry to the Champions League. Milan, six points off third-placed Roma, are among several teams expected to battle for one of those places.
Meanwhile Menez, who broke the deadlock for Milan on 20 minutes and added a second before half-time, was delighted with his two-goal haul.
"I waited a long time for a night like that, it's been a really difficult period for me," said the Frenchman, who initially made a huge impact at the club following his move from Paris Saint Germain in the summer of 2014.
"I'm delighted to score twice, but the most important thing is we reached the final.
"When you're out for so long, you start thinking a lot of negative thoughts, but I have to thank everyone, from the coach to the club and my teammates for all their support.
"Now I want to look ahead and, even though I'm not at 100% yet, try to give it everything I have."
Playing up front with Mario Balotelli, Menez's brace overshadowed the performance of the on-loan Liverpool striker, who also made a rare start for the hosts and scored Milan's fifth goal at the death.
But Mihajlovic said he will be counting on both players as Milan continue their battle to clinch a place in the top three.
Mihajlovic said: "You could see that Menez and Balotelli are still a little bit short of match-fitness, and the same also applies at the moment to Luiz Adriano.
"But they will all be key players for us from now on."
Milan face a tough trip away to Sassuolo on Sunday and the Sebian added: "Let's see how things develop over the coming matches as to whether we can fight for third place.
"We've turned things around, we've reached the final, but in the league we're still sixth and we need to keep making up ground in the table."