The 33-year-old has described last Saturday as "incredible" for him after he marked what was his 400th appearance for the Toffees by scoring the winning goal in their 2-1 Barclays Premier League victory over West Ham at Goodison Park.
Osman subsequently travelled with his team-mates to Germany, and on Thursday evening they will be looking to reach the knock-out stages of the Europa League when they take on Wolfsburg, a game they only need a point from to guarantee qualification.
With Roberto Martinez's side unbeaten and top of Group H with eight points from four matches, Everton have made an impressive return to European competition so far this term after a four-season absence.
And Osman has underlined the desire in the camp for the Merseysiders to end their continental campaign as champions.
Regarding the West Ham match, the twice-capped England international said: "To play my 400th game and score the winner at the Gwladys Street End, it was an incredible day for me.
"But I think any player will tell you, we work incredibly hard all season long and you get moments during the season when things fall into place.
"I'll enjoy this while it's here, but also keep trying to contribute to the team - I'm hoping that wasn't the only one I'll have this season."
And Osman said of the Europa League: "We are in the competition to try to win it.
"We spent a lot of last season trying to get into European competition and we managed to do it.
"Now we want to go as far as we can
We have made a reasonably good start and we're adapting quite well, so we're setting our sights high."
Osman was part of Everton's run to the last 32 of the Europa League in 2009-10.
And when asked about the size of the occasion when the Toffees play in the latter stages of European competition, he said: "To have those nights back at Goodison Park? the atmosphere that came with that was incredible.
"It's what the club wants and what the fans demand.
"We've managed to get some of that this season
But we're still not quite qualified, we still have two group games left and we need to pick up some points.
"That is what we're here for - to try to take all three points from this game if we can."
Victory for Everton over Wolfsburg - in what is their penultimate group game - will confirm them as having advanced to the next round as group winners
The Toffees will also qualify even if they lose should the evening's other Group H fixture, between Krasnodar and Lille, end in a draw
Source: PA