Preston had the bulk of the chances but it took an own goal in the second half from Sam Hutchinson to put them in front and it looked as though that would be enough to gain all three points.
Wednesday were a shadow of the side which performed so well to defeat Championship leaders Newcastle United on Boxing Day, but to their credit they pushed to the end and following Preston's inability to clear their lines, Reach hammered in his first goal for the club with seconds remaining to spark wild scenes in the away end.
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"We won one point that's for sure," said Carvalhal. "Sometimes the opponent makes it very difficult and that's what happened. Preston did that to us, they put a lot of pressure on and made it very difficult to play our style of game.
"This kind of thing happens in the Championship, so it's important to stay together like a team until the end and believe that we can achieve the minimum of one point.
"Getting the point in the last minute is something we have done before. We still believe until the last second that we can achieve points.
"At the end we had the luck that in some games we didn't have in some other games. This is football.
We missed some pace in the side. I don't want to complain, but we had no (Gary) Hooper or (Fernando) Forestieri - these are players who give us more pace.
"The reality is that we have some problems in attack with players that are out. I'm happy with the point because I know that the future will be brighter because we will recover the players and have more options."