The Parkhead club completed the quadruple domestic treble last December with a fourth successive final win at Hampden Park, overcoming Hearts in a penalty shoot-out.
The League Cup has since been lost to St Johnstone, who beat Livingston in the final, and Old Firm rivals Rangers ended Celtic's hopes of a 10th successive Premiership title win last month by clinching their 55th championship.
Neil Lennon resigned in February with Celtic struggling and the Parkhead club are in talks with former Bournemouth boss Eddie Howe about becoming the club's next manager.
However, ahead of the visit of League One side Falkirk on Saturday night, Kennedy kept his focus on the Scottish Cup.
He said: "The campaign we have had has not been as successful as in previous seasons.
"That hurts and you can feel that in the squad. It is not a good thing to deal with. We are used to success, we are used to winning.
"We are a club that demands so the competition that we will start this weekend is really important for us, for the campaign itself and for the players, for the hunger to go on and keep winning.
"You get used to winning. It becomes part of your nature in terms of striving to win as many competitions as possible.
"When you get a couple of setbacks it hurts, so it is using that hurt to motivate you to go and win the next challenge which is the Scottish Cup."