The Pilgrims went ahead after just two minutes when Robbie Williams fired home a 20-yard free-kick, but Asa Hall's stunning 30-yard strike ensured a share of the spoils.
"It's been a tough few years for all of us here - including the staff - and it was important that, this season, we have done what we needed to do," said Fletcher. "I am honoured to be manager of this club, because it means so much to the community."
"The support all season - home and away - has been tremendous but all the praise for staying in the league, under immense pressure, goes to the players. They have been superb and I am proud of them.
"We got a good start and could have had a couple more before their player hit a worldy and they hit the post but we always knew it would be tough.
"We got the result we needed and now that gives us some breathing space. I am delighted."