The opposition, the Newport-Gwent Dragons, wore specially-commissioned shirts with the symbol woven in.
The snub is surprising because the home of Ulster Rugby, Kingspan Stadium, includes a war memorial. An arch at the entrance was erected in tribute to players killed in World War One and World War Two.
Ulster have, so far, refused to explain why the players didn't wear the symbol but said the Dragons and Cardiff Blues were the only clubs to wear a poppy of all those included in the six Guinness Pro12 fixtures over the weekend and the team observed a minute's silence ahead of the game.
The club said, as is usual, a wreath will be laid at a service at its war memorial arch at the Kingspan tomorrow.
Angry fans blasted the absence of a poppy on the Ulster jerseys as "shameful".
One said the team had shown a lack of decency and respect.
On Saturday, Londonderry-born footballer James McClean was booed relentlessly for not wearing a poppy during a match at Old Trafford.
Former Ulster player Nigel Carr said it was wrong not to wear a poppy.
"It is common - and the opposition team, Newport, had poppies on - and it was typical at sporting occasions over the weekend," he said. "I'm presuming it was some sort of oversight.
"The situation here is slightly different in that there is not the same sort of consensus as to the appropriateness of wearing a poppy. That said, I would have thought in current times there is a growing recognition of the sacrifices that people gave in two world wars.
"I think it would have been better had the Ulster team displayed poppies as well."
Mr Carr, an Ireland international, had his career cut short at 27 because of injuries sustained in an IRA bomb attack.
He and fellow players David Irwin and Philip Rainey were en route to a training session in Dublin before the 1987 Rugby World Cup. The bomb killed Lord Justice Sir Maurice Gibson, Northern Ireland's second most senior judge, and his wife, Lady Cecily Gibson. The three rugby players were on the same stretch of road at Killean, Co Armagh, but escaped serious injury.
Mr Carr said the poppy commemorated not just the dead of two world wars, but those killed in more recent conflicts such as Afghanistan.
"It would have been better, more appropriate and in keeping with current trends to appropriately recognise the significant sacrifices that people have made," he added.
"It includes those who have lost their lives recently in places such as Afghanistan. It would have been right for Ulster to recognise that."
Numerous Ulster fans vented their anger online.
One posted: "We are probably the only club in the UK that has a war memorial in our ground and they can't even wear a poppy on Remembrance Sunday. Shouldn't be playing today in the first place."
Another wrote: "I await with interest the full explanation as to why Ulster Rugby do not see fit to honour the men who gave their lives fighting the greatest evil the world has ever known, among them those who died fighting to liberate Bergen-Belsen death camp. The lack of respect is simply shameful."
A third said: "Nothing to do with politics, it's to do with common decency by a club to show respect for others who gave everything so this world could be a supposedly better place."
DUP MP Jeffrey Donaldson called on Ulster Rugby to provide an explanation.
"I hope Ulster Rugby will make its position very clear because on Remembrance Sunday there would be an expectation that the team would recognise those who gave their lives," he said.
In a statement issued on Monday morning, Ulster Rugby said: "Ulster Rugby players and supporters respectfully observed a minute's silence prior to the fixture against Newport Gwent Dragons on Sunday.
"Kingspan Stadium has a permanent War Memorial Arch, which pays respect to those fallen during WW1 and WW2.
"Each year Ulster Rugby pays respect in its usual and traditional manner with a memorial service at the arch, during which a wreath is laid by the Ulster Rugby President.
"This year’s service will take place tomorrow, (Tuesday).
"Wasps played Gloucester in the Aviva Premiership yesterday and neither club wore a poppy on their jerseys.
"No other Guinness PRO12 club, with the exception of Newport Gwent Dragons and Cardiff Blues, wore a poppy on their jerseys this weekend."
In an earlier statement the club said only the Dragons wore the poppy in the weekend fixtures.
The previous day McClean was booed for refusing to wear a poppy during a match against Manchester United.
He was part of the West Brom team which lost 2-0 at Old Trafford. While all the other players appeared to be wearing poppies, it was absent from McClean's jersey.
The home support raucously booed the winger.
Meanwhile, Celtic manager Ronny Deila criticised fans who chanted through a minute's silence yesterday ahead of the 4-1 league win at Ross County.
Deila said, after seeing a Leigh Griffiths double help his side to victory: "It is something the club maybe say something about, but personally it is disappointing."