It is late night and I am already feeling sleepy, but I don't want to skip my exercises for the day. Is it going to affect the output? I am not too worried about it, but it would be good to know.
It's generally not an issue unless you're at the "numb limbs" level of sleep deprivation. When you're that tired, the odds are good that your head is not entirely in the game, and you run a higher risk of doing unsafe actions ranging from exceed your ROM to over-using your muscles to forgetting to put clamps on the ends of the weight bars. If you're ever unsure, add a bit of warmup stretching and cardio. It may help you wake up and, at the worst, it will put you in a safer situation if you just conk out in the middle of it. Better to fall asleep during a pushup than when benchpressing.
I also would not recommend exercising right after a catnap, intentional or unintentional, for the same reason.