Newcastle squandered several opportunities to take the game away from their hosts after Ollie Phillips had scored an early try and Matt Thompson had dotted down from a rolling maul.
The Falcons, without a crop of their stars through injury and with Toby Flood taking the mantle as their playmaker at fly-half on his return from the World Cup, led 18-6 going into the last 10 minutes of the tie.
But through a series of penalties amid an eager late rally by Gloucester, James Simpson-Daniel scored twice and Willie Walker added two points to bring the scores level.
"We were shaky in the last five or 10 minutes and I wasn't too happy with some of the crucial decisions that went against us," said Fletcher.
"I had a word with the referee afterwards and I will have to look at them again.
"I'm not whingeing. We got beaten heavily last week and I thought the referee was outstanding, but today he made some poor decisions at the end that cost us.
"We're bitterly disappointed. When they score in the last minute of the game to equalise, you do feel robbed.
"Gloucester are a good side with lots of internationals, and that was probably our best performance (of the season)."
Gloucester head coach Dean Ryan, having made nine changes to his starting line-up in a bid to assess his options going into the Heineken Cup, was not happy with the resulting display.
"I'm disappointed as I thought that group could get through that game and push for selection going into Europe and we didn't achieve that," he said.
"In the end we were looking for Simpson-Daniel to do something special and we should have done things easier a lot earlier."