The Finn served as number one for much of Allardyce's eight-year stint at Bolton Wanderers, before the pair were reunited at Upton Park in 2012.
At 38 years old, Jaaskelainen believes coaches at both clubs have helped prolong his career.
"I think there are a lot of little factors that come together for that," he told West Ham's official website. "I really like to work with Big Sam and the way he has brought science into the game.
"When I came to him at Bolton we were a Championship side then and he built the team up slowly and brought in people to make sure we were looking after ourselves and preparing ourselves properly for the match on a Saturday.
"I have been very lucky to have two good goalkeeping coaches. First 13 years at Bolton with Fred Barber and here I am spending a second season with Martyn Margetson. They are both top coaches.
"Experience as a goalkeeper is important for me and the main aim is to be consistent. You know you are going to make three or four mistakes during a season. Sometimes they go into the back of the net and sometimes they don't.
"You just have to recover from that and keep focusing on the right things. As long as I work my hardest during the week, whatever happens on Saturday is because I have worked my hardest in preparation."
Jaaskelainen has kept four clean sheets in West Ham's opening seven fixtures this season.