Elisa "cries like an old woman" because she is absolutely crushed because she realizes that she has been duped by the tinker and that he was not interested in her chrysanthemums at all. He had only pretended to be interested in Elisa talking about them in order to get some business from her (some pots to mend). What had been an awakening of emotions for Elisa was now a huge disappointment. Elisa realizes that she simply cannot be anyone different from who she is on her little farm with her husband. She is "trapped" there and will never be able to get her husband to see the aesthetic beauty of her flowers that she loves so much.
She cries like an old woman because she is defeated and she is weakened and powerless to go back and change it. She is defeated in the sense that the man from the repair wagon manipulated her and she read into it erroneously, thinking that he actually related to her and even took an interest in what was important to her, almost flirtatiously, when in the end, all he wanted was a sale. In a sense it confirms that her husband is not the only man she has trouble understanding, and that the differences between men and women are universal. This realization makes her feel more alone than ever way out on that farm with no one who understands her, like an old woman who has lived past her generation and who some may consider "obsolete."
I believe that Elisa "cries like an old woman" because when she met with the tinker and offers him some of the shoots of her chrysanthemims, she was not simply just offered the tinker chrysantemum shoots to take with him but she was also offered herself to him. When she discovers that he has thrown the flower shoots away on the side of the road she has to come to the realization that he has not only rejected the flowers and thrown away something very special to her but he has also rejected her, casting her to the side of the road as well. There is also pain in the fact that he used her (he duped her as he would a simply woman, by using pretty words, flirting with her and pretending to care about what she was saying –something many men would have done during that time–something she thought herself above.) She is defeat in the knowledge that all men cannot be trusted and therefore she has no way off the lonesome, isolated ranch in Salinas Valley, California. In a moment she is confined by the limitations and confinements she so desperately longed to escape.
This realization leaves her feel more alone and trapped than she ever has. Like and "old woman" who has outlived her prime and usefulness and is left with nothing to do but spend her days awaiting for the slow hand of time to claim her.