England had to hold their nerve to prevail by 25 runs at the Sir Vivian Richards Stadium, where maiden one-day international centuries by their Joe Root (107) and the hosts' Denesh Ramdin (128) made for a high-scoring and tense match.
After England's 303 for six - Jos Buttler also made 99 - proved just enough for a first series victory in any format since last August, Broad found himself answering questions about the mid-innings ball change.
"I am baffled by it," said the captain, who confirmed the umpires informed him why the ball was being changed.
"That's what they said ... then I bowled three cross-seamers with the ball they gave us, and the same wear was arriving on that ball.
"So I said 'take a picture of that one as well'. I saw no logic to it at all.
"I made my feelings pretty clear out there, as politely as I possibly could - without risking too heavy a fine."
It is unclear whether Broad was warned, a measure which in any case lasts only until the end of the series and is therefore already lapsed.
"I don't think they're saying we've tampered with the ball.
"I think they're just saying it's unnatural wear."
After marking his first ODI series in charge with victory, Broad was thankful that England still managed to edge the match after more than one umpiring decision he felt might have cost them.
Hinting in those circumstances he might have found it impossible to keep his thoughts to himself, he added: "There were a few decisions that could have changed the game today, but fortunately we got over the line
"If we'd lost this game, I think I'd have been suffering a bit of a fine."
The confusion over the ball change will not spoil Broad's celebrations, after such a tough winter for England so far.
He added: "Not at all - we've won the game. It just made it a little bit harder for our bowlers ..."
He made it clear, however, he was still in the dark about the exact reasons for the ball change.
"I have absolutely no idea ... it's not like the ball was 'reversing' anyway," Broad said.
"I was bowling cross-seam deliveries, and throughout the three games we've played here the ball was roughing up - little bits of leather were coming off it.
"Everyone was aware of that.
"I'm very confused as to why it was changed - and made my confusion well-known.
"They gave us a ball that was 10 overs old, and Ramdin started getting hold of that ball a lot easier."
Broad was delighted with England's overall performance, one clinched when Tim Bresnan bowled Ramdin with a perfect yorker to have him last out.
He said: "I think we held our calmness pretty well.
"It was still a lot of runs. We still won by 26 runs, which is a decent amount in one-day international cricket."
As for Ramdin, who was twice dropped and had an early caught-behind scare off Broad, he added: "Once he survived his first ball, it was a fantastic knock.
"It was as good as you will see in one-day cricket.
"(But) I thought we showed unbelievable nous to play ourselves in and hold ... to score off the last 10 like we did.
"The way Rooty and Jos played won us the game in the end."
On Bresnan's final delivery, Broad said: "It was a brilliant yorker, but it was that far of going for four as well - missing the leg-stump.
"Bresy's strength is yorker bowling, and when under pressure that should be the ball he goes to. He bowled brilliantly today.
"Obviously this is going to lift the boys. This group we've had in Antigua, the morale has been awesome throughout the whole two weeks.
"The guys have held themselves brilliantly to come away with a series win."
:: Root will have an x-ray on his heavily-bandaged right thumb, after being hit by Ravi Rampaul when he had made just a single.
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- Denesh Ramdin