Cardiff narrowly missed out on the Championship play-offs last term, finishing eighth in the table.
But under new head coach Paul Trollope, Pilkington thinks the Welsh side are capable of better.
"We fell just short [last season] and we were all really disappointed with that. We felt we had the squad to get in the play-offs definitely," he said.
"It's going to be a tough season again, just like it was last year, but hopefully we can be right up there come the end of the season."
Pilkington, 28, scored Cardiff's first goal in their 4-0 friendly win at Shrewsbury on Saturday.
The Republic of Ireland international played in attack, having moved from the wing to a central forward role last season.
Pilkington made the transition under former Cardiff boss Russell Slade, who was replaced by Trollope in May.
Trollope had been working under Slade before then, and Pilkington believes that smooth transition has helped the Bluebirds in their preparations for the new campaign.
"The gaffer was working with us last season so we know how he works," he added.
"We know what he's about and we know we have to be on our toes all the time.
"He's come in and changed a few things. It's been good up to now so hopefully we can carry on working really well."
Cardiff City forward Anthony Pilkington believes the Bluebirds can challenge for promotion this season.