The Argentine forward also insisted that the championship race is still very much alive at this early stage of the season.
He said: "It was a beautiful game, we could have won, and they also could have won.
"We seek to win but it's not easy. We played against Madrid and we knew it would be very complicated. We were close to ending only five points above.
"We went to look for the result but we knew we had in front a very good Real Madrid team, with very good players. We're still eight points clear but we know that there is still much to play for."
Messi and Ronaldo are level on eight goals in the race for the golden boot in Spain, with Atletico Madrid striker Radamel Falcao in the lead with nine goals in seven league games.