A7 is a decent hand heads up, its not the strongest though. You did have your opponent beat heads up but only my a small edge. Your opponent still had a 40% chance of winning with 5 cards to come. You lost and you got beat, but it wasnt a bad beat. Bad call by your opponent? Yes, but what are you going to do, right?
A bad beat is when your hand loses to huge underdog. Losing to someone catching a flush or an opponent ended straight is not a bad beat. Losing to a one outer is.
Take this scenario for example that I witnessed at a casino tournament.
Its the first hand. Starting chips is 5,000 and blinds are 25/50.
Player to the right of me is mid position and raises it to 200. I fold and the player on my left calls. The table folds to the raiser. The flop is A 5 6, with not suits matching. Raiser checks, caller checks. The turn is a 5. Raiser bets out 3/4 the pot, caller reraises big, OR goes all in and the caller calls.
Person on my right shows 55 for quads.
Person on my left shows 66 for a boat.
They had both flopped a set.
The river is a 6.