Luke Shaw gave England a dream start with the earliest ever goal in a European Championship final, but Leonardo Bonucci levelled in the second half to force extra time before Southgate’s men lost 3-2 on penalties after a 1-1 draw.
Playing on home soil for all but one of their matches, England had restored the feelgood factor in the country by booking a second major tournament final appearance in their history and first in 55 years since their World Cup triumph.
“The players gave everything they could have, not only tonight but throughout the whole tournament,” Southgate told a news conference. “They should hold their heads high.
“They are a team who have pulled together, given the country some incredible evenings. They have made history several times in the tournament. They played so well in a first half of a final when the expectation was so high.
“They have done more than any other team in the last 50 or so years. They should be proud of what they have done.”
Arsenal teenager Bukayo Saka’s miss from England’s fifth penalty proved costly, leaving the country with a record of two wins from nine major tournament shootouts.
“The penalty takers are my call,” Southgate said. “We worked on them in training. It is not down to the players. Tonight it has not gone for us, but we knew they were the best takers we had left on the pitch.
“Of course, it is heartbreaking for the boys but they are not to blame for that, it is my call as the coach who takes penalties.
“He (Saka) is not alone. He is such a super boy who is so popular with the whole group. He has had an incredible tournament, and he will continue to be a star.
“Tonight, in a final, he performed exceptionally well. We have to be there to support him, and I am sure he will get a lot of love from outside.” (Reporting by Peter Hall; Editing by Ken Ferris)