England were beaten 2-1 by Spain in the Euro 2024 final, going down to a late Mikel Oyarzabal goal.
Despite the result, which means England have now lost two Euros finals in the past two editions, Bullingham was effusive in his praise.
In a statement released shortly afterwards, Bullingham said: "We came to Germany to win the tournament, and we didn’t want it to end this way. We are all hurting tonight, but we should be incredibly proud.
"I would like to thank Gareth, (assistant manager) Steve Holland, all of the players and the support team for their huge commitment and hard work to try to win the trophy for the country. They will be more disappointed than anyone to fall just short.
"This is our fourth major tournament final in four years for the Three Lions and the Lionesses, and our ambition to win major tournaments is stronger than ever.
"Our wonderful fans have supported us with pride and passion here in Germany and back at home. Everyone involved with England wants to make the country proud, and we really appreciate their support."