Joe Lewis was particularly impressive in the visitors' goal but the hosts prevailed in extra time, Jack Cork nudging the Lancastrians back in front with a header and Ashley Barnes converting a late penalty.
Dyche also provided an update on Wood, who came off with a knock, and bemoaned the "changed" transfer market as he admitted that several signings have failed at the last moment.
"Aberdeen were excellent, it was a really tough game," Dyche told BT Sport. "They came to take us on, not defend, we needed a bit of luck.
"Their keeper was superb, one of his saves was world class. I thought we were probing at 1-1 but it's still pre-season and we were a bit loose. Chris Wood came off, we have to be careful. He had a tight hip and it's still pre-season for us.
"It would be very helpful for us to bring players in but it's very tough for us in the market and we are 24/7 at the moment. We've had a few players almost done and then they haven't gone through so there's no point talking about them until they are signed. The market has changed."
Up next for Burnley in the Europa League is a third qualifying round tie against Istanbul Basaksehir.