The National Bus and Rail Union has said the "mayhem" on some Dublin Bus and Bus Éireann routes today "should have been predicted" by the National Transport Authority.
Level 5 restrictions came into effect at midnight, limiting capacity on public transport to 25% of its normal load.
There was "mayhem" trying to accommodate passengers on a number of bus routes this morning as a result, general secretary Dermot O'Leary of the NBRU told RTÉ's Drivetime.
He said the cut in capacity is having a greater impact now than in the early stages of the pandemic due to schools, construction and more retail being open.
He said many buses departed their first stop this morning at full capacity.
Mr O'Leary said there are enough buses in the fleet currently in operation to satisfy demand, but he said the peak period should be stretched, through staggered starting times for schools and workplaces.
He said the NBRU wrote in May to the then Taoiseach as well as the leader of the opposition about staggering start times for schools and workplaces and he said both responded positively.
Earlier today, Mr O'Leary revealed there had been several "pinch points" at locations where passengers had tried to board Dublin Bus services in large numbers, with further capacity constraints on a number of Bus Éireann services "where demand has outstripped the Level 5 reduced capacity".
"Thankfully (thus far at least) no confrontation or conflict has been reported, though we are extremely conscious that frustration can lead to such a scenario", he said.
He acknowledged that passengers could not be blamed for striving to get to work at a time that suits their needs as opposed to when services "may, or can be scheduled".
He reiterated the NBRU's call for a clear plan to accommodate those required to travel for essential services, and to police capacity restrictions.
In a statement, the National Transport Authority said there were capacity issues on some services, particularly on buses in the Dublin area.
Last night @dublinbusnews teams updated onboard signage to reflect the move to 25% capacity on public transport.— Ray Coyne (Please wear a face covering 😷) (@ray_dublin) October 22, 2020
⚠️We are operating a full service but capacity is limited to 17, so allow extra time
⚠️Public transport is for essential workers&essential travel. pic.twitter.com/7ZhHKEQrSS
The NTA said it was engaging with the Department of Transport and the operators "to identify particular pressure points with a view to responding to them and addressing them where possible".
"We would continue to ask people to avoid travelling at peak times and only to use public transport for essential purposes.
"We continue to encourage people to walk or cycle where possible."