It would be an understatement to describe that defeat against a team struggling to stay clear of relegation as a disappointment for a side who are desperately trying to stop their Glasgow rivals from matching their record of nine successive championship titles.
"It was just one of those games which has no explanation." Cadete said. "You want and need to win but end up losing. Even when Peter Grant and I both hit the crossbar in the first half I didn't give up hope.
"If you hit the bar in the first minute of a match and think it will not be your day, why bother playing the other 89? We were 1-0 down for 75 minutes at Rugby Park earlier this season but won 3-1, and I kept hoping we could do that again."
Paolo Di Canio was sorely missed by Celtic after the Italian helped inspire last Thursday's Tennents Scottish Cup quarter-final victory over Rangers at Parkhead. "You always miss quality players like Paolo, but injuries happen to every team," Cadete said.
The striker wants Celtic to make it up to their fans by repeating the cup success over Rangers, when the sides meet again in the League at Parkhead on Sunday, to keep their title hopes alive.
"We must forget the Kilmarnock game. We can't change it. We've one game to think about, which is Sunday's, and the fans deserve to see another win over Rangers," he said.
Di Canio is still rated doubtful for Sunday with the hamstring injury which forced him off at half-time after scoring a penalty against Rangers last week.
Celtic will open contract talks this afternoon with three players who could walk out of Parkhead for nothing this summer. Tosh McKinlay, Peter Grant and Malky Mackay will all be out of contract at the end of the season.
Raymond Sparkes, their agent, will open discussions on their future with Celtic's financial director, Eric Riley. Any foreign clubs who want to sign Mackay and McKinlay for nothing when their deals run out will be watching with interest.
"There are options other than Celtic open to the players and this is just the first stage of talks," Sparkes said."I can't speculate on how they might go. It is an initial chat and we will take it from there."Reuse content