The Bees went ahead in the 26th minute through midfielder Marcus Bean, who followed up at the far post after Romain Larrieu had brilliantly saved Michael Spillane's header.
Argyle drew level in the 38th minute when Rory Fallon headed the ball in the air and spectacularly volleyed home following an angled cross from Onismor Bhasera.
Spillane's 67th-minute strike from the left was then turned in on its way to goal with Bees striker Charlie MacDonald claiming the final touch.
Reid said: "We weren't great. I didn't think it was a game that we deserved to get beaten in, but I don't think it was a game we did enough to win.
"When you concede off dead ball situations - which I keep harping on about - then you are not going to do well.
"When you defend you have to defend solidly. The keeper has made a save off the first one and we haven't picked up the second ball, they have picked up the ball too easily."
Source: PA
Source: PA