The Irons had slipped down towards the bottom three following some inconsistent form, which included a home loss to Stoke and defeat at Hull, before pulling off an unexpected 3-0 win at high-flying Tottenham before the international break.
It does not get any easier for Sam Alladryce's men with the visit of big-spending City, but Jaaskelainen feels Saturday's late kick-off could prove to be the launching pad for a climb back up the table.
"Spurs was a great win at a great time because we were drifting towards that bottom three and we didn't want to stay there for long," Jaaskelainen said on the club's official website, www.whufc.com.
"We need to keep going, but if you look at the Man City game, if we can get anything out of that then it could be a turning point for us and make it a decent start because at the moment it is an iffy start."
The Finnish shot-stopper added: "Playing-wise we have done very well, but we have just been missing a little bit of luck and maybe one or two decisions have gone against us."
Jaaskelainen, though, accepts the Irons will need all of their resilience to get the better of Manuel Pellegrini's expensively-assembled squad.
"If City turn up and play their best it is going to be extremely difficult for us to do anything, but we will see," he said.
"Last season our home form was fantastic, but this season we have had two defeats already so we want to make sure that if we can't win the game, we don't lose it, that is our main aim.
"I wouldn't take a draw now, but if things don't go our way and City plays a good game, it is going to be hard to beat them, but we have to make sure that we are hard to beat as well."
Forward Carlton Cole could come straight into contention after rejoining the club on a three-month deal, having left in the summer.
"I am available for selection," Cole told West Ham TV. "I will train all week with the team and then it's just up to the manager to see what he wants to do. Hopefully I will make the bench and take it from there.
"Obviously I take pride in playing up there alone and helping the team to try and get results.
"That's what I'm going to try and do.
"It's no secret how I play. I'm obviously very physical and try to be a presence up front and impose myself on defenders, create space and nick a few goals as well.
"I hope I can do that up until Christmas and see where that gets me."
England Under-21 midfielder Ravel Morrison grabbed the headlines at Portman Road on Tuesday night, where he scored and set up another in the 5-0 thrashing of Lithuania.
And the 20-year-old Manchester United academy graduate cannot wait to tackle City this weekend.
"I'm very excited because obviously I used to play for Manchester United but I never played against their first team so I'm really looking forward to it," he said on the club's media channel.
"Of course we can cause a shock. We're a great team and we should have had a lot of goals this season, but for some reason we haven't.
"Against Tottenham we managed to get the goals which have been missing which was pleasing. The defence has been solid so if we carry on doing what we're doing we can cause an upset."