Maurizio Sarri dismissed the supporters' frustrations following a defeat to Manchester United which leaves him clinging to his job as Chelsea manager.
Goals from Ander Herrera and Paul Pogba earned Ole Gunnar Solskjaer a sixth successive away win and a place in the FA Cup quarter-finals, against Wolves.
Sarri was subjected to jeers, boos and chants to be left in no doubt the strength of the Chelsea fans' feelings towards him, just seven months since his appointment.
Chelsea fans joined in as United supporters sang "you're getting sacked in the morning" and sarcastically applauded predictable substitutions in opposition to the possession-based tactics the 60-year-old Italian favours.
Asked if he had heard that chanted at him before, Sarri said: "No. For everything, there is a first time."
The Italian added: "I am worried about the results. Not about the fans.
"I can understand the situation and our fans, because the result wasn't really good. We are out of the FA Cup, so I can understand. But I am worried about our results."
Chelsea have little time to dwell on the defeat, with Thursday's Europa League last-32 second leg with Malmo followed by Sunday's League Cup final with Manchester City and next Wednesday's Premier League clash with Tottenham Hotspur.
Whether Sarri sees out the run of fixtures remains to be seen.
"If we are able to win three or four matches in a row, it will be really very easy [to change the negative mood]," Sarri added.
"I was really very worried when I was in League Two in Italy. Not now."
A change of manager has had the desired effect for United, who enjoyed an 11-game unbeaten start under Solskjaer before defeat to Paris Saint-Germain.
A seventh win from seven away games since the Norwegian's appointment on December 19, in place of Jose Mourinho, was the ideal response.
Solskjaer said: "You want to see a reaction. There's a balance between being too eager after losing a game, so this was brilliant.
"We've got to build on the positives. We play Liverpool next week, but Chelsea, Arsenal and us will fight for that fourth position [in the Premier League]. This was about getting through to the next round."
The 12-time winners next face Premier League Wolves in the last eight, with neighbours Manchester City going to Championship Swansea City.
Watford host Crystal Palace and Millwall host Brighton & Hove Albion.
The ties will be played over the weekend of March 16 and 17.
