The purpose of using the scientific method in psychological experiments is to be sure that the insights gained from those experiments will be as valid as possible. The scientific method helps to accomplish this because it helps to make sure that research is done in a systematic way.
If the scientific method is not used, experiments are not really experiments. Without the scientific method, they are no more than random actions or collections of anecdotes. The scientific method helps to ensure that the experiments are carried out in such a way that their conclusions can be tested by others and, thereby, can be shown to be valid or invalid.
The point of psychological experiments is to find out things about human thought processes that are objectively true. Using the scientific method allows researchers to be more certain that they have found the truth. It does this in large part by creating experiments that can be replicated by other researchers and whose findings can be falsified. If other researchers can copy an experiment, the experiment can be done multiple times to ensure that the results are consistent. If the conclusions are falsifiable, they can be proven wrong. This, too, allows researchers to determine what is objectively true.
The scientific method is a good way to be as sure as possible that researchers are finding facts that are objectively true. Since this is the goal of psychological research, the scientific method is very important for experiments in that field.