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There's nothing wrong with the way you did it except that you killed off your own traffic when you took the old site down. You could have kept benefiting from the traffic to the pages indexed on the old domain if you had used a 301 permanent redirect.
Try searching for "301 moved permanently" and you'll find some great resources.
A 301 would also be more satisfying for your users as you could point them to comparable content for what they were looking for when they searched.