Scott McGleish's penalty and a Carl Fletcher free-kick put Orient in control before Yannick Bolasie halved Argyle`s deficit.
Home goalkeeper Roman Larrieu was sent off for handling outside his area and Alex Revell scored from the subsequent free-kick before converting Charlie Daniels' left-wing cross in the 89th minute.
"We shot ourselves in the foot. I thought we started quite brightly and played some good football but then we conceded the penalty," said Reid. "Then we go 2-0 down to a free-kick that goes through the wall.
"I thought we started the second half really brightly as well, squeezed on them. Joe (Mason) was unlucky, hitting the post, and then we got the best goal of the game. But it typifies our season that then we had a sending off and then it's always going to be hard against a side that has good movement and rotated really well in the middle of the park.
"Then at 3-1 down you are chasing the game, so I was disappointed. The players have worked hard but you can`t afford to give goals away at any level and that's what we did. It's not a learning process because it keeps happening. Terrible mistakes have cost us."
Source: PA
Source: PA