The Staffordshire outfit, whose highest Premier League final ranking of 11th came in 2009/10, have six more matches to go this term and are looking good for clinching 10th spot.
Eleventh-placed West Ham and 12th-placed Aston Villa both have a game in hand over them, but Mark Hughes' men moved six points clear of those clubs with Saturday's 1-0 home win over Hull.
The gap between Stoke and ninth place - presently occupied by a Newcastle side that have six fixtures left - is also six points.
And regarding the standings, Ireland said: "We have to keep chasing ninth - that's all we can do and it's what we want to do.
"We don't want to settle for 10th, because we don't want to get complacent. We want to keep going and going.
"You never know - there could be something riding on the last game of the season for us at West Brom, which is what we are hoping.
"We don't want to go there and just have a friendly game. We want to go and hopefully be in a position to secure ninth."
Stoke are coming towards the conclusion of Hughes' first season in charge in fine form, with the Hull triumph being their third win in a row and fourth in their past five games.
Ireland has emphasised that there is a strong feelgood factor around the Potters camp at the moment, and is looking ahead to next weekend's match at Chelsea - beaten 1-0 at Crystal Palace on Saturday - in an optimistic mood.
"The morale is big at the training ground and we are heading in the right direction," said the 27-year-old Irishman, whose season-long loan switch to Stoke from Villa in September was made permanent in January.
"We can go to Chelsea with their confidence knocked and ours sky-high, and we have to take advantage of that.
"Hopefully we can capitalise and win there as well."
Stoke forward Peter Odemwingie scored the winner in Saturday's contest, netting for a third successive game when he intercepted a misplaced pass by Hull's Ahmed Elmohamady in the 62nd minute, advanced to the edge of the box and fired in.
Hull boss Steve Bruce - whose side dropped to 14th, seven points clear of the relegation zone - was left lamenting that error, which followed on from Tigers defender James Chester's own-goal in Wednesday's 2-1 defeat at West Ham.
And Bruce also rued the visitors' inability to make the most of their chances in an encounter he felt they should not have lost.
Stoke goalkeeper Asmir Begovic did well to keep out a Tom Huddlestone drive and deflected David Meyler effort, and Liam Rosenior headed over between those attempts when it seemed he really should have done better.
Bruce said: "Begovic has proved he is a top-class goalkeeper - he has made one or two really good saves.
"But it was there for us. It was always going to be difficult at Stoke after playing with 10 men for a large period on Wednesday night.
"But we are disappointed that we have gone to West Ham and then come to Stoke and not picked anything up.
"We certainly deserved to. We certainly didn't deserve to get beaten in this match."