The Sunderland striker has managed five goals in six games since his summer switch from Wolves, which was enough to secure the Player of the Month award.
Fletcher was delighted with the honour but the Scottish international, who is set to represent his country for the first time in nearly two years in their up coming World Cup qualifiers, insists that results are more important than individual accolades and is keen to continue his rich vein of form.
He told Sky Sports: "I'm delighted for a little personal award. We've had a good start to the season, so hopefully it continues.
"I wanted to hit the ground running as there was a lot of pressure on me coming to this club with the price tag and stuff."
Fletcher, who joined Sunderland for around £12million in the summer, hopes to improve on his goal record for relegated Wolves last season, where he managed 12 goals.
He added: "I think I'll just try and better last season, to be honest. I think I got 12 last year, so if I beat that I'll be happy."