It was confirmed on Thursday that 42-year-old Lennon has parted company with the Bhoys after four years and three Scottish titles amid speculation that he was about to do so.
The hunt is now on for a successor with former star striker Henrik Larsson immediately installed as the bookmakers' favourite.
However, Republic of Ireland international McGeady, who played both with and under Lennon during his time at Parkhead, knows the new incumbent faces a tough task.
Asked how much of a blow the Ulsterman's departure was to the club, the Everton winger said: "It's a big blow. Now Celtic will obviously be looking to replace him with someone, but the big question is who do you replace him with?
"That's the first question, which candidates are out there? You start looking straight away.
"It will be a difficult job because Celtic is a massive club and success is a way of life, you have to go and win every game, you have to go and win every trophy you compete in, apart from the Champions League.
"If you are not winning two trophies a year, you are seen as a failure."
McGeady, however, admitted the news did not exactly come as a shock, even if the timing of it may have done.
The 28-year-old said: "To be honest, it's not really come as a surprise because of some things I've heard from a few people, that he was a bit unsettled and had probably kind of done all he thought he could do with the club and maybe was looking for a new challenge down in England somewhere.
"Maybe the Celtic fans wouldn't be shocked by it either, but obviously to just hear 10 minutes ago that he had resigned was a little bit of a shock in that sense.
"Ever since he took over at Celtic from when I was there, he was brilliant. I played with him - he was difficult at times to get on with as a player, but as a manager, I can't speak highly enough of him.
"He was fantastic when I was there and led the club to many trophies in the last four years.
"Maybe he just thinks it's time for himself to get down to England somewhere and have a new challenge."
Some bookies were quoting Larsson as an odds-on favourite to get the job within minutes of the announcement.
The former Sweden international is currently in charge of Falkenbergs in his native country, but McGeady is confident there would be popular support for his appointment.
He said: "That would go down well, I think, with the fans, very well. I was lucky enough to play alongside him and he is so highly thought of at Celtic.
"He's in every fan's greatest ever XI, an absolute legend, so if he was to get it, I think the fans would be pretty happy."