A freak fielding deflection off Ben Stokes' bat that raced to the boundary saw England awarded six runs with three balls to go in the final over on Sunday.
Stokes then tied the score at the end of regular play. Scores were again level in the resulting Super Over, and England won a first World Cup because they had hit more boundaries during the final.
Taufel told Fox Sports Australia that the umpires had made a "clear mistake", as the batsmen had not crossed for their second run when the ball was thrown in by the fielder.
"They should have been awarded five runs, not six," he said, adding that England's Adil Rashid should have faced the second-last ball instead of Stokes.
Giles, asked if he was concerned, said Monday: "Not really."
The former England spinner added: "You could argue the last ball that (Trent) Boult bowled was a full toss on leg stump and if Stokes hadn't just been looking for two, he probably would've banged it out of the ground anyway.
"We are world champions; we have got the trophy and we intend to keep it."
Taufel, a five-time winner of the International Cricket Council's Umpire of the Year award, sits on the Marylebone Cricket Club (MCC) laws sub-committee, the worldwide custodian of cricket's sometimes obscure rules of play.
The Australian defended the match umpires, who he said had to make a complicated judgement, and added it would be "unfair" to say their call had decided the tournament winner.
Heartbroken New Zealand captain Kane Williamson said: "It was a shame that the ball hit Stokes' bat.
"Unfortunately that sort of thing happens from time to time. It's a part of the game that we play."
England, who have often cited a humiliating defeat by New Zealand at the 2015 World Cup as the catalyst for their climb to the top of the one-day international rankings, finally have a World Cup win to go with their three losing appearances in the 1979, 1987 and 1992 finals.
New Zealand were also seeking to win the trophy for the first time after being well beaten by Australia in the 2015 showpiece.