How do you know if an insignificant P value is because of chance error or because the sample size of the data is too small? I have always thought that an insignificant P value is the product of chance causing variation in the data. However when I was watching a talk on a study, the presenter mentioned how the insignificant P value meant that the sample size of the data was too small to make any conclusions rather the being the product of chance error. How can you tell if an insignificant P value is caused chance error or small sample size then?

The long answers are mostly correct, but only address your specific question indirectly. The short and direct answer is that you can gather evidence that will help you decide if your sample size is too small or if your data are misleading (due to error or due to natural sampling variation) ONLY by gathering another sample of data.
The reasons that you need another set of data can be had from the longer answers.
