Wales came from behind after trailing 11-6 at half-time at Kintetsu Hanazono Stadium. Harry Robinson scored a second-half try while Dan Biggar kicked 14 points before replacement Rhys Patchell sealed victory with a late penalty. Despite this, Wales were out-scored two tries to one as Japan responded through Michael Broadhurst and Yoshikazu Fujita.
McBryde said: "I was hugely proud. I was a bit disappointed that we put ourselves in that position to start off with, but once we were in that position, the boys really dug deep. I can't fault them. They really got together and showed character and true grit to come through that second half."
He added: "We had seven new caps today against an experienced Japan team that had obviously targeted this game. We were in a tough place at half-time, so the fact we have come out with a win is hugely encouraging."
Biggar levelled the scores after Ayuma Goroumaru kicked Japan ahead with two early penalties when Wales number eight Rob McCusker was sent to the sin-bin, before Broadhurst crossed at the end of the first half as the visitors struggled in scorching heat.
Wales captain Bradley Davies said: "Obviously hot weather is a factor, there's no hiding from that. We had trained here all week and knew it was going to be tough going into it.
"A lot of us hadn't played for about a month. You can do as much training as you want, but until you are out there in the middle it's not the same. It was tough.
"It took us a while to adapt, but we sat down at half-time and had a chat and the way we adapted in the second half and ground out a result was very pleasing."
Biggar kicked Wales ahead on 60 minutes before Robinson raced clear for his second try in only two international appearances. Japan wing Fujita scored a try 10 minutes from time that was converted by Goroumaru but his earlier misses proved critical.
Japan coach Eddie Jones said: "It's a game we could have won and needed to win. I'm very proud of their effort but Test match rugby is all about taking opportunities. We had chances and didn't take them and that's why we came second."