The Blues are now on a run of five successive draws.
Yet once Shaun Wright-Phillips had breathed new life into his team just before the break, a successful comeback mission always looked likely.
And with Kolo Toure and Craig Bellamy both finding the net before the hour mark, City looked set for the perfect send-off ahead of their trip to Abu Dhabi this week, where they will carry out some promotional work in addition to tackling the United Arab Emirates on Thursday.
Instead, Mark Hughes is left wishing most of his senior men were coming as well - rather than flying off for their respective international commitments - after substitute Kevin McDonald arrived unmarked to tap home Fletcher's nod-back.
The City manager said: "It is frustrating and disappointing because we got ourselves into a winning position.
"We have to learn to see games out because we have drawn two games at home from winning positions.
"Maybe it was a consequence of the effort we put in before that, because we worked exceptionally hard to get ourselves in front.
"But we did not do the right things at the right times."
He added: "I would like to think we will get some credit for the way we came back but the late goal did take the edge off it.
"It is a poor result because we have come back from a situation most people probably thought was beyond us.
"We are 11 games into the season and we have done OK, no more, no less. There are times when we look what we are; a team coming together and trying to gel."