Allardyce's arrival at the Black Cats has sparked an immediate improvement in their performance levels, and they picked up their first win of the season with a 3-0 victory over Newcastle United last weekend.
Sunderland have now conceded just one goal in their first two matches under Allardyce, and Fletcher believes that the experienced boss's organisational skills have been a big help.
"He is probably the most organised manager I have worked with and he demands a lot from everyone," he said. "He works hard on the training pitch and is very hands on, which is good."
Allardyce has never been relegated in his career as a manager, and there is growing optimism that he will be able to keep Sunderland up.
The Wearsiders made a slow start to the season, but already they look a more compact outfit, and seem much harder to beat.
Their win over Newcastle at the weekend should provide them with plenty of confidence, and they could move out of the relegation zone if they are able to win their next fixture.
Sunderland take on Everton on Sunday afternoon, and if they can take the three points from that game, the positivity building around the Stadium of Light will increase further.