The east London outfit have only lost once in their opening four games, with Jaaskelainen keeping three clean sheets in the process, following his summer move from Bolton.
The former Finland international told the club’s official website: "It has been a very good start to the season.
"You can see we are continuing to build together as a team and to have kept three clean sheets in four games is obviously a very good start.
"But to come away from home against a good side in Norwich with another clean sheet and another point is very pleasing."
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The 37-year-old proved his worth to the team once more with a string of impressive stops against Norwich on Saturday, but insists he was only doing his job.
He continued: "Sometimes you have to be there to help out the team in certain situations and on Saturday I was able to do just that.
"The biggest disappointment for us was to not get a goal in the first half and that maybe in the second half our attacking play didn't have the same quality it could have."
Jaaskelainen now insists he is focused on working hard to repay the faith shown in him by West Ham.
"For me it is always the same wherever you are," he explained. "I try to work hard throughout the week to make sure I am ready for the game on Saturday.
"It helps that I have played in the Premier League before and I already know Sam [Allardyce] and his backroom staff.
"I really like the way they look after their players and hopefully I can repay them by keeping my performance levels at the same heights they have been so far this season. As a goalkeeper it is all about consistency."