Chiefs went ahead in the first half thanks to a rocket from range by Reeve Frosler but Kwame Peprah levelled matters for Pirates early in the second stanza.
Eric Mathoho snatched the winner for the Glamour Boys nine minutes before time, but Baxter felt his side did not manage the game well.
"I thought it was a tough derby, I thought we did well in the first half, we were well organised, I thought we had a good control of the game," Baxter told SuperSport TV.
"Paradoxically we scored and then Pirates threw the kitchen sink at us and so, they got a goal back and bombarded us, going behind us, into us, second-balls, flick-ons.
"And we get the second goal, we thought it's all over but it's not because we don't manage those last ten minutes properly and Pirates worked their socks off.
"And unfortunately on a day like that we could end giving away the victory and we gotta be better than that."
Chiefs were forced to make a couple of changes, including Khama Billiat late in the first stanza and Leonardo Castro just after coming on early in the second stanza.
"We were constantly jumping up and down on the bench because of players that were struggling or we had to change them eventually," Baxter went on.
"We had already decided that Leo [Leonardo Castro] would go on for Lebza [Lebogang Manyama] because Lebza is not at full fitness yet but we wanted that false nine, two quick lads Khama [Billiat] and Keagan [Dolly] to challenge their two centre-backs when Lebo drops in that space.
"We got that quite nicely in the first-half, we didn't get Lebo enough on the ball and when Leo comes on and does his hamstring then the whole picture changes," he said.
"Then you feel like you're trying to manage the game from the bench, which is impossible, they got to manage it on the field, we made the changes that we could make and at the finish we made the change to go with three centre-backs because the game is played in our penalty area from their centre-backs."
"I'm happy and delighted for the supporters and everyone involved at the club for the good result but we have to be better than that."