Wanderers finished nine points above the drop zone last time around and the Finnish shot-stopper is keen to finish as high up the table as possible.
Jaaskelainen feels slow starts have hindered them in seasons gone by and is setting a target of 15 points from their opening 10 Premier League fixtures.
The 35-year-old feels that, with the platform of a solid start, then Owen Coyle's side can realistically challenge for a top-10 place come the end of the season.
Bolton only mustered five clean sheets last season and Jaaskelainen believes that increasing that number and tightening up at the back will only aid their quest.
"The main thing for us is to have a good start and, in the first 10 games, we need to get around 15 points because in the last three years that is what has been letting us down," he told the Bolton News.
"If we make a good start, then we can look for a top-10 finish.
"We made loads of individual mistakes and that's why we didn't have that many clean sheets. There was only five last season and that wasn't good enough.
"With the manager bringing a lot more confidence to players hopefully we can show that during the season and that will result in more clean sheets."