The rider’s manager Barry Symmons spoke of his shock at the tragedy.
“He was a really nice guy who was well-respected by his peers and someone with a true talent for road racing,” said Mr Symmons.
The rider’s wife Brenda and his father were present at Saturday’s meeting organised by the North Armagh Club.
“This year he was really looking forward to being on top and riding winning bikes,” added Mr Symmons.
“He was was doing what he loved and he was doing it very well.
“He rode the MV (Agusta) for us last year and at some considerable personal cost (as well).
“It is tragic that this has happened.”
Before the accident, Finnegan had claimed an impressive win in the open race at Tandragee.
“That was his first win on a Yamaha for quite a long time. He was really on top of things and looking forward to the rest of the day,” recalled Symmons.
Finnegan’s fellow-competitor Ryan Farquhar said after the accident that oil had been coming out of the Dubliner’s bike.
“His back tyre was covered in oil,” added Farquhar.
The Motorcycle Union of Ireland chairman Alan Drysdale described Finnegan as “one of the star riders of recent years”.
“It is a tragedy that this has happened,” added the MCUI official.
“It is impossible to make it (the sport) totally safe.
“A lot of effort went in from the North Armagh Club.
“The incident that Martin had will be investigated to see if any lessons can be learned.”
Another rider, John Donnan, was killed in last year’s Tandragee event but Drysdale said that it was “too early” to say if the future of the meeting could now be in doubt.
Former competitor Phillip McCallen said he knew Finnegan very well and added that “he was really looking forward to this season”.
“I spoke to him a week ago and this season, for the first time in a few years, he felt he had really competitive machinery.
“The Tandragee course is near to my home and I know the club have worked hard to make the circuit as safe as possible.
“Maybe they need to limit the capacity to 600cc for the public roads, but we are still seeing a record number of newcomers taking up the sport and it is still popular with the public.
“Martin’s passing is a terrible, terrible loss to the sport and it is a dangerous sport, there is no getting away from that.”
In Saturday’s accident, three spectators were also injured, two males and one female.
The woman was taken to hospital with head injuries but none of the injuries suffered by the spectators are thought to be life-threatening. The meeting was abandoned after the accident.
Married father-of-one Finnegan was competing this year for the JMF Millsport Yamaha team.