In a word, no. It has nothing to do with antioxidants, and I implore you not to start thinking about nutrition outside of simply eating a balanced, nutritious diet free from excesses. Whilst it is possible that diet is responsible, it is unlikely; the average diet in industrialised countries provides approximately double the normal recommended intake of protein, for example, or roughly the amount recommended for elite strength and power athletes.
What you are most likely experiencing is fatigue based upon your workload and level of conditioning. To put your experience into perspective, an old study of muscle fatigue asked a group of subjects—all novices—to perform a single set of bicep curls to failure. Muscle biopsies were taken and markers of muscle damage measured periodically thereafter. The average subject experienced muscular soreness for 4-5 days thereafter, with the worst still feeling soreness after nine days. However, markers of muscle damage were detectable in one subject as much as 60 days after performing that single set!
That is not to suggest that we require such great periods of time between bouts of exercise. However, it does demonstrate just how long muscles can take to recover fully. And numerous studies have demonstrated that there is no measurable difference in hypertrophy between individuals who train once, or multiple times per week, for example.
All training is essentially about finding the right balance between work and rest, and difference between the casual gym-goer and the elite strength and conditioning coach is their ability to balance those variables correctly.
If you are weaker during your second training bout than you were during your first, it indicates plainly that not only have you not developed, but that you have not even recovered. You are regressing and inviting injury. And that is because you have done too much work (volume), or you have done work that is too hard (intensity), or you have otherwise not given yourself enough time to recover between bouts of exercise (rest). Indeed, you have done all of these things, since they are all relative and related. That is, you can do a large or intense workout, provided that you rest accordingly. Or, you can do a smaller or less intense workout, and do it more often. As your conditioning improves, you will gradually be able to work more, work harder, and work more frequently.
Keep in mind that everyone can overwork, or overtrain, and that the single greatest failing of elite athletes is not doing too little, but doing too much.
So, I recommend that you either reduce the volume of your training bouts, from four sets to two sets, for example, or increase your rest from four days to one week. You are gaining nothing (very clearly) by training beyond your current ability to recover. And I strongly recommend that you read as much as you can about the concept of supercompensation.
I hope that helps.