What you have done is two experiments (biological replicates) with 3 technical replicates in each. You would not usually treat the technical replicates as independent experiments - you would take the means of the technical replicates for each experiment and compare them between biological replicates.
You can get a standard error with 2 replicates, but the error will be large (you lose power in this case as it is derived from the square root of the sample size), and as such require that there be a big difference between the biological replicates before you could say anything about their difference statistically speaking.