Exeter used six substitutes in the first replay on November 16, bringing on Josh Key for Sam Nombe at the start of extra time, having made five changes during ninety minutes - with the hosts going onto win 3-0. Rules permit just five substitutions.
A Football Association investigation was conducted and the governing body ruled the replay must be held again - on Tuesday evening in Exeter.
Adams believes that the new replay should have been staged this coming weekend - when the second round of the competition takes place and also feels that it should have been staged at a neutral venue.
Instead, City - despite being the innocent party in regards to events earlier this month - face a third long trip to St James Park already in 2021-22.
And should they go through, they will visit Cambridge United this coming weekend in a second-round tie, which would represent their seventh away game out of eight in all competitions, if you factor in the annulled first replay at Exeter.
Adams said: "We are in a situation where we were playing the tie and did not break any rules in the game and unfortunately for us, the rules were broken. The referee, fourth official and two linesmen allowed the six substitutes to happen. We all agree with that.
"That changed the flow in the game on the night. We then have to go back to Exeter to play the replay.
"If we win on Tuesday night and progress in the Cup, we then have to go away to Cambridge on Saturday at such a short turnaround. I think that is unfair and unhelpful, but it is something we have to deal with.
"I also think that the game should have been played on a Saturday when the second round of the FA Cup was taking place. I don't think for both sides, Bradford and Exeter, to play the game on a Tuesday and then play the game on a Saturday is particularly fair to any of us."
On the circumstances of heading back to Exeter for a second replay, he added: "The communication from the FA to the clubs was via email. We did have a call on the Wednesday morning (November 17) from the FA to let us know what was going to happen. But the board from the FA decide what is going to be.
"If the game had been played at a neutral venue, then we can all see that as being a sensible option. To then ask us to go back to the original venue where it took place where Bradford City, as a football club, have not done anything wrong in the situation, is a bit unfair.
"Exeter are playing at home and have their home supporters again and we have to go back down there."