The Norwegian left-back admits he never likes to lose or draw, but he would be particularly disappointed if the Cottagers fail to get the three points as favourites on Wednesday
The competition has perhaps suffered with clubs putting out weakened teams, but it still holds importance to Riise, who will be highly disappointed if he and his team-mates fail to live up their label as favourites when Odense visit Craven Cottage.
The other match in Group K takes place between Wisla Krakow and FC Twente, with a win for Fulham, regardless of the other result, being enough to take them through to the knockout rounds.
"I would be devastated if we didn't go through,” Riise told reporter.
“I hate losing and I always try to win every game I play. Obviously that doesn't always happen, but tomorrow is a match we're favourites for and it would be quite hurtful not to go through.
"It has been up and down,” he continued. “We would have liked to have been in a better position going into the last game, but, at the same time, we have our destiny in our hands. If we win we're through and that's a nice feeling to have.”
Riise, who arrived at Fulham mid-way through the Europa League qualifying campaign, has been in and out of the team for the European matches, but he’s glad to be involved when called upon.
He continued: "From my point of view, I came into the competition a little bit later than the other players, because they started early [on 30 June].
“The manager decided to rest me for a few games at the beginning but now I've played the last two.
“I want to play every match but if the manager decides to rest me then that's fine and I respect it."
Fulham’s opponents on Wednesday, Odense, are already out of the Europa League and having a poor run domestically, currently eighth, but Riise is adamant the Cottagers can’t afford to underestimate them.
“They haven't had the best campaign,” he noted. “But they have the quality to hurt any team, so that's why we have to be on top of our game.
“I'm sure we'll do that tomorrow, play our best football and get the three points.
“We're fully aware of what they can do, but, at the same time, on paper we're the better side and should win."