Kone was replaced just before the hour mark as Sunderland picked up the three points over the Blues, with John O’Shea coming on to replace him.
The change was a surprising one, but Allardyce felt that Kone had started to show signs of fatigue in the contest.
“I think the pressure of playing every single game since he’s been here made him look a little jaded to me,” he said.
“I wanted the experience of John O’Shea to secure our defensive frailties. They were there a little more than I’ve seen for quite a while, so John coming on and using his experience to block that end worked and of course more importantly at the other end were Fabio and Jermain’s goals.”
Allardyce’s switch certainly seemed to work, as Sunderland came from behind to claim the victory against Chelsea.
The Wearsiders were 2-1 down against the Blues, but a brilliant second half performance turned the match on its head.
Goals from Fabio Borini and Jermain Defoe saw them claim the three points, which has lifted them out of the relegation zone.
Sunderland can now confirm their safety by beating Everton on Wednesday evening.
Kone is expected to be fit for the clash, but it remains to be seen whether he will keep his place in the side.