The 22-year-old returned from his second injury of the season as a substitute against Newcastle at the end of April and bagged a first Barclays Premier League goal within a minute of entering the action.
Borini, who revealed that his dream is for Liverpool supporters to copy his unique celebration after he finds the net, explained his target to establish a lasting relationship at Anfield.
"If I've got emotion that comes from that club, obviously I take that emotion with me," he told Liverpoolfc.com.
"At Swansea I had three months I could never think of. In three months, I got into the hearts of the people and I could see Italian flags in the stadium - I never expected that.
"In Roma, after a long injury, I started scoring and the people were showing things in the stands as well.
"When you see those things, it gives you an emotion you can never forget. I hope I can do the same here because I'm trying very hard."
The Italy international arrived on Merseyside for a season in which Jamie Carragher has announced his retirement and Steven Gerrard has started every single Premier League fixture under Brendan Rodgers.
Borini accepted his fledgling career has differed to the path of the local pair but believes the duo are role models for young players.
"In modern football it's more difficult because you've got many opportunities to change and more distractions on what you want to do," he added.
"I left home very soon; they have played here in Liverpool, which is their home. I've already left home, I think it's different for me.
"But obviously it's something that you need to look at because not many people now, as a young player, will be able to stay at the same club for 10 to 15 years and give everything.
"I live in the short-term and I didn't expect that I could play at Liverpool and in the Premier League so soon. At 22, I would probably still be starting in Italy with some architecture or interior design subjects."
As the 2012-13 campaign nears a conclusion, Borini allowed himself to consider the possibilities for success next season - on both an individual and collective level.
The striker said: "It's another opportunity but I will start with the same attitude, because injuries happen and you just need to deal with them. It's nothing that you can control, they just come.
"Next season will be the same for my mentality and my attitude for what I want to achieve; the objectives won't change much.
"We showed that we can play against the top clubs, and away from home getting good results. We were maybe a little bit unlucky this year because we drew 2-2 in most games against the top four clubs. If we can get a few wins in there, I think we can really fight for the top four."