Nahki Wells' superbly-placed free-kick in injury time cancelled out Orient's opener from Lloyd James on the stroke of half time to ensure the spoils were shared at the Coral Windows Stadium.
Although Wells' goal - the Bermudian's fifteenth of the season - came in the final knockings of the game, there was no denying that the strike was just rewards for Parkinson's side after they had dominated the second period.
Given his team's positive display against League 1's table-toppers, Parkinson was pleased to see City collect at least something from the game for their efforts.
Parkinson said: "I don't think anyone at the game today (Saturday) could argue with the fact that we deserved at least a point out of the game.
"Even in the first half, against a strong side and playing into a fairly strong wind, I thought we played well.
"The dressing room was a flat one at half-time (after conceding Orient's opener) as much as me and Steve (Parkin) tried to be as positive as we could.
"We knew it would be testing to try and get back into the game because Orient are a hard team to break down.
"We kept knocking on the door though and eventually got our rewards.
"The conditions didn't help, but we've pinned them in for large periods in the second half. The lads stuck at it and you have to give them enormous credit for that.
"As we've said a number of times before, most games last until the 94th/95th minute and you can score at any point during that period. You have to believe you can do that.
"We kept getting in those free-kick situations because we have attackers who put defenders on the back foot. I think the one at the end was our third or fourth of the day and Nahki has put it in the top corner.
"It was a very, very good free-kick and something that he practices in training.
"Obviously we came into the game looking for all three points, but we'll take a point, we don't like losing. We know we need to turn some of these draws into wins but, in terms of today, we have put a good effort in and the lads can be pleased with the way they played."
THE FULL VIDEO CAN BE VIEWED ON BANTAMS PLAYER - PLEASE CLICK HERE