The tie produced nine goals over the two legs.
"We played very well in both games and leave with our heads held high," said Ramos.
"We played a serious game here and at home. We didn't win the title, but we gave a great performance. Barcelona were only better in efficiency because they capitalised more on their chances. Real Madrid made a great impression and showcased great attitude, so no one can reproach us anything.
"Games like these, in which titles are at stake, always give way to nerves and tension. Whatever happens on the pitch stays on the pitch. I don't want to do any comparisons. We are humble and hard working, and we're here to take Real Madrid to the very top.
"The season is very long and we're on the right path. We gradually get to know our opponents better and prepare for matches in specific ways.
"We apologise to our supporters for not bringing the title back to them. We hope they continue to support us."