Departed manager Brendan Rodgers "changed the landscape massively" at Celtic, while John Kennedy leaves "a big hole", according to captain Callum McGregor.
Rodgers resigned on Monday evening, with long-serving assistant Kennedy's exit confirmed the next day.
Martin O'Neill and Shaun Maloney have been appointed on an interim basis and are preparing for Sunday's Premier Sports Cup semi-final against Rangers after starting their temporary reign with a 4-0 home win over Falkirk on Wednesday.
"I just found out the same as everyone else," McGregor said when quizzed on Rodgers' surprise decision to quit, which was announced in a brief statement.
"I spoke to the manager maybe 10, 15 minutes after it. We had a chat, which will stay private for obvious reasons. It's a shock at the time and then very quickly you're five minutes from going to bed.
"You've got to deal with the aftermath of that. I spoke to some of the players and then we came back in on Tuesday and it's business as usual, you've got a game to play the next day."
Rodgers won four titles, along with seven cup triumphs, over his two stints as manager, with McGregor a midfield regular in the first spell and skipper for the second.
"Hopefully he'll be judged for what he's done for the club," McGregor added. "Going back 10 years, he changed the landscape of this club massively.
"The success we've had was because of the values and work ethic he instilled when he came in the first time - and that has carried us through a long period.
"Unfortunately, in football everything comes to an end. Everyone would love the fairytale end, but very rarely does that happen. Football can be brutal at times, that's just the way it is.
"As a club, we have a lot to thank him for.
"He was amazing for my career. He's done so much for me, so on a personal level I have so much to thank him for and I'm sure whatever he does next he'll be a big success."
Kennedy ended a 27-year association with Celtic, having joined as a teenager in 1999 and serving as assistant to Neil Lennon and Ange Postecoglou as well as Rodgers.
Hailing his "incredible contribution", McGregor said of Kennedy: "He took a lot of responsibility and he's someone I have huge admiration for.
"We had a really close personal relationship - and professional. He was someone you could rely on in difficult times.
"I don't think he got the credit he deserves. To be at this club for such a long time and do the job he did, it was outstanding.
"There's a big hole that will need filled. For me, it's right to acknowledge how big a part of the success he was. He was absolutely first class. I think you'll be hard pushed to find a better assistant manager."
McGregor went on to say that O'Neill and Maloney have "come in with a real positivity", stressing that the former "understands the fabric of the club".
On 73-year-old O'Neill, he added: "He's a really good person and he has good people around him. Hopefully, with a lot of hard work and little bit of luck, we can be successful.
"Right away, when he spoke to the players, he made them feel at ease and winning games is the biggest thing to help everyone."

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