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Rangers trailed at the break, through ex-Ibrox striker Kris Boyd's shot but recovered in the second half with James Tavernier's free-kick to draw 1-1.
"It's the worst display in the last 14 or 15 months," said manager Warburton.
"We move quickly and with quality on the training field and we didn't do that. We chose to go long and I don't know why."
Warburton's side, who won last season's Championship, have yet to keep a clean sheet in the Scottish Premiership this term, posting two 1-1 draws and two 2-1 wins.
"We draw with Hamilton in the first game and the end of the world is nigh," said Warburton of the expectations on his side.
"There is no shortage of desire and commitment. What we have to do is take it from the training pitch on to the match pitch.
"We have had passages of good play, Dundee second half and today second half. But we have to be better for longer.
"We have to play with a bit more belief. We looked hesitant at times in terms of our decision-making. That is very unlike us and we didn't get the ball moving.
"We have new players coming and there is maybe some gelling still going on."
Killie's Greg Taylor was dismissed for a second-half tackle on Joey Barton and Warburton said: "Joey is okay.
"I saw the challenge. We don't want to see anyone sent off, but it was a poor challenge.
"I was conscious the atmosphere was rising. He was on a yellow card, so I took him off as a precaution."
Meanwhile, striker Joe Dodoo was sent for an x-ray on his ankle after landing awkwardly early on.

Chief executive Jonathan Ford said the FAW would be working with organisers and others as safety was "paramount".
An army of fans are expected to make the trip for Wales' games in June.
They face Slovakia in Bordeaux, England in Lens and Russia in Toulouse in their first major tournament since 1958.
Plaid Cymru leader Leanne Wood called for 16 June to be made a national civic day so more fans can witness Wales take on England.
She said because the match will take place during working hours, employers should be encouraged to make provisions to allow employees the afternoon off.
Mr Ford said it was hoped friendly matches would be held in Wales before their Group B matches to give the "boys a great send-off".
The majority of home matches since 2011 have been staged at the home of Cardiff City.
The last time Wales played at the Millennium Stadium was the 2-0 defeat by England in March 2011 in front of a crowd of 69,000.
Mr Ford said: "Of course, there are some complications at home. There are concerts that happen in the summer at those stadia.
"We've got to look at that. We've got to put it all together as quickly as possible."
He said Uefa, which oversees football in Europe, took "security very, very seriously".
"Tragic circumstances here, of course, very much mentioned in the ceremony and in the draw," he said, referring to the Paris attacks in November.
"Our focus now has got to be on to the teams, but we will have many people working with us to ensure the environment is very secure for us," he added.
Mark Warburton lamented his team's first-half display at Kilmarnock, saying: "It was not a Rangers team."
[NEXT_CONCEPT]
Security will be taken "very seriously" for Wales football fans in France to watch the team at the Euro 2016 finals, the Football Association of Wales boss has said.