Michael Emenalo cited a "palpable discord between manager and players" as one of the reasons Chelsea decided to part company with Jose Mourinho.
Mourinho's second stint in charge at Stamford Bridge came to an end by mutual consent on Thursday with the Premier League champions stuck in 16th place in the table, just one point above the relegation zone
The Portuguese - a three-time league champion during his spells in England - had said he felt "betrayed" by some of his players following the 2-1 defeat away at Leicester City on Monday.
Technical director Emenalo said Chelsea's hierarchy were forced to take action with the club "in trouble".
"It was a decision taken to protect the interests of the club," he told Chelsea TV.
"While there is a huge sentiment for an individual that has done so much for the club, the fact of the matter remains that Chelsea Football Club is in trouble.
"The results are not good. There obviously seemed to be a palpable discord between manager and players.
"We felt it was time to act."
Emenalo is confident Chelsea's coaching staff can cope in the short term, starting with Saturday's Premier League fixture against Sunderland.
However, he also confirmed they are now "vigorously" searching for a permanent successor to the departed Mourinho.
"You’re not a big club if you don’t have contingency plans for situations like this," he added.
"We are a big club who has quality coaches embedded within the club. I think we will be OK for Saturday [against Sunderland].
"Make no mistake about it, the club is working vigorously and actively to make sure that the situation with regards to a managerial appointment is made as swiftly as possible."
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