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."

The Football Association, known simply as the FA, is the organisation that looks after all football in England. Similar organisations play the same role for football in Wales, Scotland and Northern Ireland.
It was formed in 1863 and is the oldest football association in the world. As the first ever football association, it does not need to call itself the "English" FA. The FA is based at Wembley Stadium in London.
It controls many different competitions, the most famous of which is the FA Cup. It is also responsible for appointing the manager of the men's, women's, and youth England football teams.
Although it does not run the day-to-day operations of the Premier League, it does have some say in English football's biggest league.
The FA has been accused of being old fashioned and out of date in the way it is run, and the people it has in power.
The government has repeatedly called for the FA to be more of a reflection of modern society, and those who play the game. It also wants the organisation to change the way it makes decisions.
The FA is run by a group of people called the FA Council, which has 122 members. Just eight of these members are women and only four are from ethnic minorities. More than 90 of the 122 members are aged over 60.
This is a big area where some people believe the FA needs to change. The government wants more women and people from ethnic minorities to have a say in how the FA is run.
Other areas that the government wants to change are for fans to have more input, and changes to limit the power and influence of the Premier League.
On 9 February, MPs in the House of Commons, had a debate about whether they believed the FA can change itself, or whether the government needs to step in to force changes.
They voted that they had "no confidence" in the Football Association to make the changes.
The vote itself does not have any powers or immediate effect on the FA, but it will be seen as a warning to the organisation that the government could force them to change if they don't act soon.
The FA faces losing getting money from the government, but is confident they can make the changes themselves to keep the government happy.
Cardiff City forward Anthony Pilkington believes the Bluebirds can challenge for promotion this season.
[NEXT_CONCEPT]
MPs have voted to say that they don't believe the biggest organisation in English football, the FA, can make the changes needed to keep it modern and relevant.