You might try tossing it in the clothes dryer with a damp towel for 20 minutes on medium heat... depending on the weave of the cotton & weight of the cotton yarn, the fabric might shrink up just a touch -- enough to close the holes. But honestly, even with regular washing & drying, I've never found that the holes closed up like they did with cotton thread. The reason it works with cotton thread is that the cotton fibers become slightly damaged by the agitation & heat and swell & shrink such that they marry together nicely. The same thing is true with wool & silk, and to a lesser degree, rayon fabrics/threads. With 2/3-ply synthetics threads, the thread can ever so slightly fray/become less tightly wound to help fill in the holes. With mono, there's only the one ply and its only response to heat is to eventually melt. Synthetics do not react to water. So unless the cotton fabric itself slightly shrinks, I don't have any ideas about how to close up those holes.
In the future, you might try making a practice sandwich with size 70/10 sharp/Microtex needle to quilt to see how that does. It's what I use with 50/2 cotton for quilting, as it makes a smaller hole. Sorry, I know that doesn't help this time. Hopefully others will have better ideas.