If the F-test for your model is measuring the significance of the model fit, then with p = 0.0737 your model is significant at the 10% level but not at the 5% level. Suggest using the model with that statement. You should follow up with test on the treatments/factors to see which have some affect on the response and which don't (your result is suggesting that changes in some explanatory variables are not enacting changes in the response).
If there is some factor that has a very small effect, try removing it from the model, that will increase the degrees of freedom for the error in estimating the effects of the remaining factors. Alternatively, if it's not too cumbersome, add one more replicate.
Before interpreting the result. it would be better to check the "Adjusted R-Squared" value. It the Adj. R-Squared value is low (for my personnel opinion; Adj R-Squared value should be at least 80 %.); it means the model was not good enough to explain the varialtion therefor caused the MSE high comparing with the MS of factors. If the Adj R-Squared value is high; we can interpret the F-value, p-value based on the confident level we pre-determined. We shall pre-determine the confident level first before we conduct the DOE.
I've had similar issues in the past.
If your p-value for the model is below 0.10, I'd take that as a good sign.
I'd be more interested in the Adj R^2, R2 (pred) and lack of fit.
What software are you using?
It is always preferred to make the model fit with a p-value of 0.05. The 95% confidence level is the most desired one. Hence the model should be made significant.