England are attempting to square the series after losing the second Test by nine wickets at Mohali. The opening match ended in a draw at Nagpur.
"We have just got to live with it (Harmison's absence) and not think of it as a curse," Fletcher said on Friday.
Harmison is the fifth member of the Ashes-winning squad unavailable for England's crucial match.
Regular skipper Michael Vaughan and fast bowler Simon Jones returned home due to injuries even before the series had started, while opener Marcus Trescothick left the squad because of personal reasons.
Veteran left-arm spinner Ashley Giles was ruled out ahead of the tour due to a hip problem.
"Sometimes these things happen. From our point of view these are huge losses as we have lost experienced players, but we just have to get on with it," said Fletcher.
England have yet to decide whether Harmison will be available for the One-day series which begins on March 28.
"We will look at him for a week, review his condition during this Test, and then see if he will be available for the first two One-dayers before making a decision if he goes back," said Fletcher.
England plan to go into the match with five specialist bowlers to ease pressure on ace all-rounder and stand-in captain Andrew Flintoff in the absence of Harmison.
"We may go with five bowlers because we do not expect him (Flintoff) to do all the work," the England coach said.
"He is a major player. We just have to make sure that we don't put an enormous pressure on him. We just cannot afford that."
India captain Rahul Dravid conceded that Harmison's absence was a big blow for England already missing key players.
"It will be disappointing for England because Harmison has been a stand-out performer," said Dravid, who is set to become the sixth Indian to complete a century of Tests on Saturday.
Kapil Dev, Sunil Gavaskar, Dilip Vengsarkar, Sachin Tendulkar and Anil Kumble are the others to have figured in 100 or more Tests.
"It's a great feeling playing the 100th Test, but the focus will be on winning the match (and the series)," said Dravid.
The Indian captain hoped his spinners would be able to pose problems for England's batsmen on a track expected to favour them early in the match.
"The wicket here has got bounce and I think it will start taking spin late on the first day or the second day," he said.
Spinners dominated the last Test at this venue in 2004, with India beating Australia in two-and-a-half days. Part-time Australian spinner Michael Clarke also struck it rich with six wickets.
The match is also special for star batsman Tendulkar, set to make an Indian record 132nd Test appearance.
"What he (Tendulkar) has done over the last 16 years, to have carried the pressure and expectations of the nation, has been phenomenal," said Dravid.
"He is still a very big hero. It's a compliment to be playing with him when he achieves another feat."