The Whitehall man was introduced to the squad by Anthony Daly but flourished under Cork man Cunningham between 2015 and 2017.
That was despite the team going through a difficult period and several established players, some of whom have since returned, quitting or being axed.
Former Dublin defender Michael Carton was one of those to leave Cunningham’s panel and claimed in late 2016 that “it was a toxic environment” to operate in.
But O’Donnell said: “This idea of a negative atmosphere snowballed and it kind of seemed to be all that people talked about. We didn’t get the results but we had lots of poor results under Daly and previous managers too. It wasn’t down to one manager.
“The manager is there to put the structure and system in place but at the end, we step across the line. Pat Gilroy is highly regarded now but we’ve had bad days this year too so I wouldn’t blame managers or systems or structures.
“This negative atmosphere (talk), I always kind of laugh. No offence, but it’s people talking outside the camp. We had an enjoyable year. Some players had issues which is perfectly fine. It’s an amateur sport, we can’t expect people to put their lives on hold.
“People want to travel, to work, to do various different things. Mark (Schutte) went to football and he won an All-Ireland, you can’t fault him for that at all.
“So I would rubbish this idea of a toxic atmosphere. It’s been discussed to death at this stage. I don’t know why it keeps getting brought up. Ger’s been gone a long time.”
O’Donnell acknowledged that having won breakthrough National League and Leinster titles in 2011 and 2013, Dublin’s form did dip in recent seasons.
“Yeah, and I suppose that’s the biggest point of frustration for us,” continued the Fitzgibbon Cup finalist with DCU. “Look at the Tipperary game this year in the league even, for the first 12 minutes or something it was 0-10 to 0-2 for us. The frustrating part was not that we didn’t keep that winning margin, but that if Tipperary scored two points we should have tagged on one ourselves whereas Tipperary got a snowball going on us and we couldn’t stop it.
“I think it’s more of a mental thing than physical attributes or skill levels. So we feel that frustration as well, that we see in training what we’re doing and the intensity of training matches and the skill levels and then it’s just not replicating on the pitch.
“It’s what Pat is working on now mainly, getting that confidence because it has been a low point, the last four or five years.”
Dublin beat Laois and Antrim in their Division 1B league campaign and outscored Galway from late in the first-half until full-time.
They also had that great start in the quarter-finals against Tipp before fading out badly.
O’Donnell is convinced they can aim for top spot in the new Leinster round robin campaign which begins at home to Kilkenny on May 13.
“I got asked a question that will we be competing for third place in the group and I would refute that completely — we use the motivation of winning the Leinster far more than we use the motivation of avoiding relegation,” said O’Donnell.
“We would consider ourselves with the Limericks, Galways, Clares. This year, probably far more so than the football, it’s as competitive as you’ll get and you probably couldn’t call who’ll win the All-Ireland.”