Saturday's 3-1 home win over West Ham means the Potters have lost only once in their last seven fixtures and they are currently 11th in the table, level on points with 10th-placed Aston Villa.
Eleventh in 2009/10 is the highest Premier League position Stoke have finished in since they were promoted to the division in 2008, and Wilson said: "The manager (Mark Hughes), staff and all the guys have been saying we want to keep this run going until the end of the season.
"We have eight games left now. All the lads are focused on picking up as many points as we can, and we want to finish in the top 10."
The victory over West Ham provided further evidence that Hughes' efforts since his appointment as boss last summer to get Stoke playing a more flowing brand of football than in previous seasons are proving successful.
They fell behind early on through Andy Carroll's header, but Peter Crouch's shot went in off Peter Odemwingie to level things around the half-hour mark and the Potters then wrapped up the win in the second half with some eye-catching play.
Marko Arnautovic slotted in at the end of a good passing move before Odemwigie smashed home to round off a counter-attack.
And Wilson said: "We were playing some nice stuff and created a few chances.
"After we got the equaliser, apart from maybe a five to 10 minute spell in the second half, I could always see us winning.
"We haven't won by two goals in a while, so it is a good boost for us."
Midfielder Stephen Ireland, back in the Stoke first XI as a replacement for the suspended Jon Walters, was a key player in the game, having a hand in all three of his team's goals.
Ireland joined the Potters on a season-long loan from Aston Villa in September which was turned into a permanent deal in January.
The 27-year-old Irishman is looking to rejuvenate a career that began so brightly at Manchester City, where Hughes was his manager for some of the time, but has since stalled with disappointing spells at Villa and Newcastle on loan.
And after Ireland's fine display on Saturday, Hughes said: "I know every time I bring Stephen into the team that he will give us quality and awareness of when to play the right pass, and he will always give you a goal threat too.
"I think (at previous clubs) he has been a victim of circumstances more than it being anything he has actually done himself.
"But his ability has always been there. I think now he is at a place where he knows he is appreciated and he knows he gets good work that will make him a better player."
Asked if Ireland would be with Stoke next season, Hughes added: "I hope so - that is our intention.
"It is something I think both parties want. We are trying to get it done."
The defeat for West Ham was their second in a row, a double which has come off the back of four straight wins.
Manager Sam Allardyce, after sticking with the same first XI for several games, made four adjustments to his line-up for the game at Britannia Stadium and admitted he may have made a mistake in doing so.
He said: "The changes were very difficult to make on the basis of what those who had played before had done.
"And it doesn't look like I should have made them to be honest - I think I might have made the wrong decision."
Following the fourth of their quartet of wins, the Hammers had 31 points from 27 games.
And, having seen his side lose the two matches that have followed, Allardyce said: "I have always told the players right from the very start - it is not about your position in the league, it is about having more points than games played, and that is diminishing again.
"We had put a nice distance between our points gained and games played, but it is diminishing and we need to stop that."
West Ham are 12th in the table, three points behind Stoke and six clear of the relegation zone.