The Gunners have made a disappointing start to the campaign, with defeat to Blackburn Rovers at the weekend adding further disappointment to a side who have suffered setbacks both on-and-off the pitch so far this term.
Frimpong earned praise on his league debut for the Gunners, despite seeing red in the 2-0 defeat to Liverpool at the Emirates, and is confident the new player brought in on transfer deadline day can quickly gel to create improvements in north London.
"We are building a new team, and I have to admit that I was pleased to see new midfielders come in on transfer deadline day. That has made things look a lot better now," he told the Sunday People.
"At the start of the season I looked around, and we were a bit short on numbers. People were playing because the manager had no other options for selection. Players like Mikel Arteta and Yossi Benayoun will help us, even if it means I find it harder to get in the team I welcome it because I want to do well.
"People have written us off this season - and obviously that 8-2 game at Manchester United didn't help. It was a very difficult situation but the manager has told us it was something that only happens once. We started slowly and at the moment we are playing catch up - but I believe top four would be a good achievement for us."
Recently committed to the Ghanaian national side ahead of England, Frimpong admits his early exit from the defeat against Liverpool was a bitter pill to swallow.
However, the 19-year-old insists he will not be changing his style of play, but will learn from the mistakes he made against Kenny Dalglish's side.
"It has been a crazy start to the season and when I was sent off it was hard to take.
"People say maybe I'm too enthusiastic and that I need to calm down, but that is the way I play and I can't change that too much. In that game maybe I was a bit too crazy, but I will learn."