Was calling a mistake?

First time posting here so I apoligize already if there's any noob stuff in this post.

Situation:
In a poker satellite at a casino and I was in the middle position. The player on my right called the blind. I receive A-K unsuited, and I raised 3 times the blind. The blinds fold, and the player to my right contemplated for a little bit and called my raise. Flop was 9h-As-7h. She thought about it for a second, and just called all in. She was second in chips, and I had about half her stack, prolly 4 or 5th in chips . I thought about it for a split second and just called. My method of thinking (from how I saw her play earlier in the tourney) is that she always slow played two pair or top pair. If she was somewhat weak, usually a semi bluff, or had bottom or second pair, she'd just bet way too aggressively. She flipped up 10-8 unsuited. Of course, knowing my luck, she catches a 6 on the river to complete her straight. Then after the play, I got up, said nice hand to her, and she said it was a mistake for me to call. And another player sort of agreed with her. I kind of walked out of there dejected, but I couldn't stop thinking if it was a mistake. To me, it wasn't a mistake, I had a made hand, and her overbet with all the chips seemed like the right play, but she just got lucky....what do you guys think?

You did the right thing, don't let her talk down to you like that! You had top pair top kicker on the flop, and more often than not, you will win that hand. That even makes me feel bad that she would tell you that it was a bad call, I would make that call almost every time,
unless you have a really good read on her, and you can for sure put her on a set of nines or sevens, which from the way she was playing seemed unlikely.

[RiverDood]

Once you end up at the flop, with an Axx board, your line is just fine. Punch up the hands on twodimes.net and you were a 62% favorite to take down the pot. Yes, you didn't know for sure what she had. But her range included a lot of weaker aces and weaker PP. Against most possibilities, you were well ahead. Only a flopped set would have been trouble -- and you can't run from every possible scary scenario.

But let's take a second look at how you got there. Your 3BB raise was timid and invited trouble. With a limper in the hand, you should be betting at least 4BB to give her and the BB crummy odds for playing on with weaker cards. The 3BB isn't enough to do that. By the time the action gets to her, there's 5.5 BB in the pot and she only needs to pay 2BB to stay in. That invites her to call with almost anything.

You don't want that. T8 is actually a much peskier hand for you than AQ. (Think about how the hand would have played out with a 863 flop, or a T72 flop, etc.)

Bet 4BB or 5BB instead before the flop, and she doesn't call your initial bet with such a middling hand. If she's got junk, you take down a small pot and live to play lots more. If she's got a weaker A, and calls you, you're right where you want to be.