As used to be the case - and when you are watching from the stands or even less than up-to-the-minute TV coverage, you'd just go 'that was tight' and forget about it. The problem of course is that endless replays from multiple angles by the TV broadcasters have meant that the armchair viewer was better informed than the on-pitch officials. The managers (never mind the viewers) were watching that coverage and moaning.
I think SteMerritt's idea is the best one, and one I have suggested before. Each manager (or captain?) has two (or three) appeals. If they think a decision is wrong, they can ask for a replay. Appeal correctly and you retain the appeal and the decision is reversed. Appeal incorrectly and you lose the appeal. Once you have used all of your appeals, that's it. Exactly like cricket. The beauty of this is that the onus is on the manager to make the decision to review. If they get it wrong, it's their fault. If they have lost all of their reviews before there is a dodgy decision that it their fault. If they didn't appeal for a decision that was wrong, that is their fault. It takes the pressure off the refs to a large degree, and might go at least a small way to make managers think about blaming the refs for their own shortcomings.
Of course, it will also reduce the amount of VAR stoppages there are in a game - at present it can be pretty endless and saps some of the excitement out of the games.