It's difficult to give an exact answer without actually observing the light and performing measurements. I have a theory, though.
Your peripheral vision is hyper-sensitive to changes in light - an evolutionary trait that provided quicker reactions to predators sneaking up on you. As such, even the tiniest fluctuations in light can be registered with your peripheral vision; much more so than your primary field of vision. In this case, it may well have been that the light was flickering very subtly, or at a very high frequency, which your primary field of vision could not pick up. When your peripheral vision was in play, it immediately spotted the flicker.
This is reliant on a principle called the flicker fusion threshold, which essentially states that there is a threshold of various light properties (including flicker frequency, colour, intensity, etc.) at which an eye begins to distinguish a steady light from a flickering one. Research has demonstrated that species who have high rod density are good at picking up flickering, whereas species with low rod densities have a much poorer threshold. Cone density doesn't seem to factor in very much, since flickering is primarily a change of intensity rather than hue.
This transfers into the human eye, since we have a high rod density (and low cone density) at the edges of our retinas, i.e. in our peripheral vision. If you had the eyes of another species (as creepy as that would be) with a high rod density, you may well have been able to detect the flicker quite easily with your primary field of vision.
To directly answer your question - yes, I believe this is primarily the "fault" of the eye, rather than the brain. The brain has a role in identifying the flicker at a subconscious level, in terms of fight or flight response, but the eye is responsible for providing the elevated sensitivity at the peripheral.