The Cherries, who sit at the top of League Two, saw a five-match winning stretch come to an end with a 2-1 defeat at Hereford on Tuesday night.
Teams around them did not capitalise on their defeat, so Eddie Howe's men remain four points clear at the summit and Fletcher wants to extend their lead.
"The run was always going to come to an end, but things were going so well that I think we thought it would never end," Fletcher told the club's official website.
"It's how we react to the defeat that is important. We have a very tight-knit unit and that has won us games, and we need to start winning games again.
"We need that spirit because we have some hard games coming up and none harder than Port Vale on Saturday, which is always a hard place to go."