How about a "1 review per game", option?
If teams feel a certain decision has gone against them, they can appeal. Then and there. The player in question, indicates to the captain of his team about the foul/offside/penalty/yellow card etc, who inturn speaks to the referee about the decision to review the incident. The game is paused, and reviewed on live camera (As in, the replays are shown on TV), very similar to the 3rd umpire review system in cricket.
The teams can only enable 1 review per game, and if they get it wrong, they lose their appeal in their next game. They are not carried over.