Simeone struck after nine minutes at the Olimpico Grande Torino, converting the rebound after his initial header came back off the post, and the hosts controlled the contest from there despite failing to add a second, sending the Granata through to face Monza in the next round. Speaking to Sportmediaset afterwards, Abate reflected on a difficult opening test.
"We knew it would be a tricky game, like it is for everyone in August. The team had a very good first half, in the second we slowed down a bit too much, we needed to have the composure to see it out, but I'm satisfied. There was a lot of emotion, I'm really happy to be at such a prestigious club. The work will be hard, but important."
The coach praised the attitude shown by his squad in his first competitive game in charge, while also flagging clear areas for improvement before Torino's Serie A opener against Milan on August 23.
"I liked the team's desire to improve, the lads have the hunger and the curiosity. We have so much to put into the concepts. This group has shown me it has the desire.
"We need to improve a lot in our solidity and in reading the game. We have wide margins for improvement and it's a point we need to keep pressing on."
Abate, who spent much of his playing career at Milan, also addressed his connection to Torino's opening-day opponents.
"AC Milan? That's my past, my life for so many years. It's the club that made me a man and allowed me to play on important stages. I'll give everything I have to the granata world and I hope to give my fans a great moment of joy."
The win sends Torino into the sedicesimi of the Coppa Italia against Monza, while the club now turns its focus to the Serie A curtain-raiser against Milan, the visit of Abate's former club to the Stadio Olimpico Grande Torino a week on Sunday.