Wednesday's 10-goal top-scorer saw his tame 55th minute spot-kick comfortably saved by Villa goalkeeper Jed Steer.
It proved a big turning point as the visitors scored two goals in added on time from Albert Adomah and Tammy Abraham to condemn Wednesday to their first loss under manager Steve Bruce.
Versatile midfielder Reach told The Star: “Steven is the one out of anyone who you would want to have the ball in his hands, but these things happen.
“Unfortunately it didn’t go for us. On another day we might have scored that and seen the game out, but that’s football.
“We will just have to go again and try and win on Tuesday.”
Fletcher partnered Gary Hooper, who opened the scoring in the seventh minute with his first goal in over 15 months, in attack.
But Villa star John McGinn cancelled out Hooper’s opener.
“Fletch is just as disappointed as everyone else," insisted Reach. "He didn’t get on the scoresheet and as a striker he will be disappointed but, it’s a collective effort; we win together, and we lose together.
“It’s a disappointed dressing room but we’ve got to forget about that now. We can’t change it."
The Owls, who have slipped to 12th in the table, six points off the play-off positions after losing only for the second time in the last 18 league outings, return to action at home to ninth-placed Nottingham Forest on Tuesday.
On their top-six chances, Reach said: "We have to win all of our games.
“There are good sides up there and they are not going to drop points every week.
“So we’ll go again. We can take positives in that we dominated large parts of that second half (against Villa).
"Unfortunately we couldn’t get the goal and they did us on the break but we will dust ourselves down.”
Dominic Iorfa (thigh) has been ruled out of the Forest clash and Wednesday could also be without the services of Barry Bannan (hamstring) and Rolando Aarons (ankle).
Meanwhile, the Owls’ Under-18s cruised to a fifth consecutive win after thumping Ipswich Town 4-0 at Middlewood Road. Goals from Conor Grant (2), Charles Hagan and Liam Shaw maintained Wednesday’s title push. Andy Holdsworth’s side are a point behind leaders Leeds United in the U18s North League table with three matches left to play.