A stuttering start to the campaign left the Hammers teetering above the foot of the table before their impressive 3-0 victory at White Hart Lane.
Jaaskelainen is looking to add to the points tally against Manchester City this weekend, and is confident a positive result could have a bearing on their season.
"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.
"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.
"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 admits he is expecting a tough encounter with City on Saturday though, but the stopper believes home advantage could help West Ham.
"If City turn up and play their best it is going to be extremely difficult for us to do anything, but we will see," Jaaskelainen added.
"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."