The Great Britain pair led throughout the first five rounds of the competition but missed out on the title by less than a point in a high quality competition at the Aquatics Centre.
Daley and his Plymouth Diving partner Goodfellow finished with a score of 444.30 points, but the experienced German pair of Sascha Klein and Patrick Hausding grabbed gold with their final dive, finishing with a total of 445.26.
Ukraine’s Oleksandr Gorshkovozov and Maksym Dolgov were third with 429.75 points.
Daley said afterwards: “It’s not the result we wanted, but I can’t say it’s necessarily a bad thing. There’s a lot of positives to take from it.
“We were only two points off our personal best. I said to Dan ‘don’t worry, let the Germans have this one and we’ll be coming to get them at the Olympics’. It was less than a point in the end. Half a point from any judge throughout the whole competition could’ve changed it.
Goodfellow added: “I am a bit gutted. We wanted that gold medal, especially in front of a home crowd.
“It just gives you that fuel to do better in the Olympics.”
It was Daley’s second medal of the championships, having won gold in the three-metre mixed event with Grace Reid the day before. He will dive in the individual event on Sunday.