McKenna's decision to leave on 10 June, after guiding the club to three promotions, blindsided the Portman Road dressing room, with O'Neil appointed just under a fortnight later.
"Yeah, it was very much a shock - none of us players saw it coming," O'Shea told eadt.co.uk. "That was a tough time for a lot of the group because most of us, myself included, have had some of the most enjoyable seasons of their careers under him.
"He's definitely a legend for a lot of people in the town and we'll all be forever grateful for what he's done. So, yes, there was surprise and there was a bit of sadness too. But we're all experienced enough to understand that you can never have a manager for too long in football.
"There's always change in this game. Now it's time to move on and for something new. It's exciting. There's never a time to look back at this football club. This football club's always looking forward and building. The next step in this project is to try and stabilise ourselves in the Premier League and get this club back to fighting for what it should be fighting for."
O'Neil, who has previously kept both Bournemouth and Wolves in the top flight against the odds, has already declared himself "100% sure" Ipswich Town will beat the drop this season, and O'Shea says the early signs under the new head coach have been encouraging.
"Really good. I first spoke to him, actually, a couple of years ago because he tried to sign me at Wolves, so I had a feeling for what he was about and how he wanted to play," O'Shea said.
"I knew straight away that it wasn't going to be a massive transition from Kieran. They're very similar in the way they want to play football. They're two great, young, hungry managers who want success. Obviously, it's been nice to speak in person and understand what his aspirations are for the season and what he wants from us as a group. He's brought new staff in. A lot's changed. It's only really Reg (Rene Gilmartin) and Sone (Aluko) that have stayed from the coaching staff. It's been different, but it's been great.
"It's just nice to have new ideas and a new energy around the place. We really want to stay in the division. We really want to do well this season. We know what we can do. It's exciting."
O'Shea also says he likes what he has seen so far of Emersonn, the club's new record signing.
Elsewhere at Portman Road, Boniface has left for League One side Leyton Orient, becoming the O's eighth summer addition after coming through the youth ranks at Chelsea and joining Ipswich in February 2025.
The 20-year-old England youth international impressed during the Under-21s' debut Premier League 2 campaign and had featured in seven senior matchday squads without making his competitive bow for Ipswich.
Head coach Richie Wellens, himself a former Ipswich loanee, said: "Every player we have had from Ipswich has been excellent and I hope that Somto will be the next to join that list. He is predominantly a left-back but can play at right-back, too. He is quick, athletic, he can go past people and is the profile of full-back that we want. Tactically, he is very adaptable and he adds a lot of pace to the team. I'm really looking forward to working with him."
Boniface links up at Brisbane Road with former Ipswich academy graduates Armando Dobra and Idris El Mizouni.