Bolton go into the tie looking for a boost in their collective confidence ahead of their return leg against Marseilles at the Stade Vélodrome next Thursday.
Jaaskelainen blocked out the French side on Wednesday night with the game finishing 0-0, leaving the door to the last 16 ajar. "It is a massive week for us," said the Finnish goalkeeper. "We want to stay in all competitions and, hopefully, win something.
"Marseilles are a good side but so are we. We play the top teams week in, week out in the Premier League and get good results. The main thing is we kept a clean sheet, so there is everything to play for. We have every chance of nicking a goal and going through."
Jaaskelainen made a string of superb saves, the highlight being a breathtaking stop from the electric Mamadou Niang after he had burst through.
"I am confident facing one-on-ones," said the Bolton keeper. "You just have to make the right decision. Luckily for me, I called this one correctly."
On a controversial night at the Reebok Stadium, Bolton were denied four penalty appeals by the Portuguese referee Olegario Benquerenca in the round comprising the last 32 participants.
A blatant handball by Frédéric Déhu went unpunished while the former Manchester United goalkeeper Fabien Barthez escaped after piling into the back of Kevin Davies.
Déhu was also seen to make contact with Stelios Giannakopoulos in the face and the Bolton winger also went to ground after Lorik Cana's challenge.
However, Giannakopoulos held his hands up after the Cana incident. "He did not touch me. It is a bad habit I have brought from Greece," said the player, a member of Greece's European Championship-winning side. But Stelios added: "I deserved a penalty after getting an elbow from the centre-back. It was a clear elbow on my chin. The referee or linesman should have seen it."
Bolton last won the FA Cup in 1958 and the winger is aiming to end that barren run. He said: "This is a very important competition and we want to go through to the next stage. It has been so long since Bolton were in the final and it would be great to get to that level.
"But we know it is going to be very hard against West Ham. They are a good side and are on a very good run."
Bolton's manager, Sam Allardyce, is boosted by the return to the squad of the midfield duo Gary Speed and Hidetoshi Nakata. Speed, 36, has featured in two matches after a six-week absence with a knee injury. Nakata was suspended for Wednesday's game.
The former Blackburn Rovers striker Matt Jansen may come into the frame for the West Ham match after recovering from the knee problem that forced him to miss the Uefa Cup tie.Reuse content