The Swiss forward, who scored nine goals in 14 games in the second half of the last campaign including a hat-trick against Hamilton, agreed a three-year deal with the Easter Road side earlier this month, and insisted he wants to aim for second spot once again.
The 23-year-old admits it will a bigger ask this time around, pointing to the improvements other teams have made during the close season.
“When you see the quality in the team and how we played [last season], it is realistic,” Kamberi said.
“It is not easy - Celtic are very strong, Rangers will be stronger than last season, Aberdeen and Hearts... It will be a tough season but we also have enough quality in the team.
“The important thing is to have a good start. If we can win the first two or three games, that will be perfect,” he added.
The former Grasshoppers frontman reckons Hibs are capable of anything so long as they maintain a focus.
“If we train hard and do well, then anything is possible. We don’t have to play under pressure. We just have to play like last season and take it game by game,” he continued.
• READ MORE - Hibs boss glad he took ‘gamble’ on Kamberi and Maclaren
“The goal is to finish like last season or better. But it is too early to say now. We have to prepare well for the European qualifying games.”
Kamberi also revealed the chance to continue working under head coach Neil Lennon was a big draw in his decision to return to Leith.
He said: “I like working with the gaffer a lot. He gave me the trust I need. I was clear I wanted to come back and [Lennon] was a big, big part of that.
“It was a big decision for me to make but when I knew he was here, I was happy and ready to come back.”
Kamberi scored in the 2-1 defeat to Hearts at Tynecastle that ended Hibs’ hopes of finishing second, and also prompted Lennon’s furious post-match outburst in which he branded the display “unacceptable” and raised questions over his future at the club.
• READ MORE - Done deal: Hibs sign Florian Kamberi from Grasshoppers
But the former Swiss Under-21 international reckons the Northern Irishman was right to lambast his players, explaining: “It is better to have a coach like this. He wants you to improve; he is a winner and he wants us to be winners.
“Against Hearts, he was right. We played very bad, and we lost the chance of second place. It is good to have a coach like this, who has fire, who wants to bring on every player, every day.
“It is a great pleasure to work with Neil. It is great for the club.”
Kamberi is also keen to force his way into the Swiss national team, after watching them close in on qualification for the World Cup knockout stages after a 1-1 draw with Brazil and a 2-1 win over Serbia.
“If they can draw 1-1 with Brazil, they can win against other big teams, so anything is possible,” Kamberi said.
“The Scottish Premiership is not an easy league, so if I am doing well here, I have a chance [of being part of the team]. That’s the goal for me.”