The SPL champions secured the Double, edging out the Fifers courtesy of Jean-Joel Perrier Doumbe's 84th minute winner.
And Irishman Kenny added: "We hung on and I can't fault any of our players for their efforts.
"They were terrific, but overall I can't really complain as we were beaten by a strong side."
Meanwhile, Darren Young admitted that the Pars, for all their efforts, came up short in the final.
"We all gave our very best today," said the midfielder.
"The team was confident going in at half time as we worked Celtic hard but unfortunately didn't create very much in front of goal.
"We simply have to bounce back from this disappointment - releagation hasn't really hit home yet, but we'll just have to get used to it over the summer break.
"We've beaten some good teams in this cup run, so we have to focus on that to motivate ourselves again to bounce back to the SPL next season."