It's not unusual for the sclera (white part of the eye) to bleed where the tiny needle is inserted to inject the Avastin solution into the rear area of the eye.
It's not your retina that was bleeding onto the tissue; it's likely just a blood vessel in the sclera that was nicked by the needle and bled a bit. Similar to when you have a flu or other vaccine - sometimes the skin bleeds a bit because a nearby blood vessel was opened by the needle's passage.
If it was a slightly bigger blood vessel, it might have bleed until the pressure was applied. The sclera is relatively opaque so the doctor can't see those blood vessels to avoid them, and they are so small they can be hard to see. The needles used for Avastin injections are so thin they usually don't cause any bleeding, but it is not uncommon. Nothing to worry about; it just takes a little while to go away and the surface of your eye might be a bit discolored as ValveJob says until the blood cells on the surface dissolve.
I had two Avastin injections in 2012 for a CNV caused by myopic degeneration. The first one must have broken a blood vessel in the white part of the eye (not serious but very ugly). I think I remember putting a Kleenex next to my eye and getting blood on it.
The Avastin injection is used to treat eye diseases such as diabetic retinopathy, retinal vein occlusion and wet-aged macular degeneration. It works by inhibiting the growth of abnormal blood vessels in the back of the eye. The Avastin targets a specific type of protein considered to cause abnormal blood vessel development. By backing the stimulus it can stop the blood vessels leaking and growing.