The former England midfielder was unveiled as Mark Robins' replacement on Thursday.
Lampard has signed a deal through to the summer of 2027 with the Sky Blues ahead of his first match in charge against Cardiff on Saturday.
Coventry are currently 17th in the Championship, two points above the relegation zone.
Meanwhile, Lampard has not been in the dugout since leaving his caretaker role at Chelsea in June 2023.
His previous tenures at Derby, Everton and with the Blues have seen some fans doubt whether he is the right man to succeed Robins.
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Lampard has now responded to those concerns after being asked about scepticism surrounding his appointment.
Speaking to talkSPORT's Adrian Clarke, he explained: "Listen, they're entitled to their opinions. I've got no worries about that.
"I think in the modern day, if you become a manager, you can't be too prickly. You can't probably listen to a lot of that.
"So thanks for telling me. But, you know, it's a serious fact that in this job, you are held up to high account even before you start the job. That's the reality of it. I've got no problem with that.
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"I've been used to it as a player for many years and as a manager and working in a job.
"I have a confidence in myself and I want to show how well I can do the job.
"I've also had a lot of support and found out there's a lot of Coventry fans where I didn't even know in the last two or three weeks down in London, walking down the Kings Road in certain areas.
"So it was another realisation of the history of this club and the strength of its fan base.
"So they can't all love me. They probably never all will love me, but I'll do my best to bring them the team they want. And then maybe they'll sort of like me."
The 46-year-old was also asked if any pressure comes with following in Robins' footsteps.
Lampard added: "Well, I don't know. What I have got is a lot of respect for him and the job he did.
"I actually used to cross paths with Mark a bit when I was actually managing at Derby and was always very polite, always very respectful.
"So a really good football man who did a great job here.
"So I'm not sitting here to try and play myself off against him, tell him I'm going to do these great things.
"I think he's probably a good son of a good manager, who is a manager that's left good roots for you to try and continue in your own way.
"So I'm very thankful for the work he's done here. I've got complete respect.
"I need to earn my respect through the work that I do. Simple as that. I'm quite humble about that. I'm not coming here as some kind of unveiling.
"This is, you know, shouting from the rooftops what I want to do. I want to get to work."
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Robins' second spell as Coventry boss saw him take the club from League Two to the Championship play-off final during a seven-year tenure.
He also guided the Sky Blues to the semi-finals of last season's FA Cup before losing on penalties to Manchester United.