The Barcelona star feels his side did enough to emerge victorious Sunday and has rued the team's lack of fortune.
The Catalans fell behind early as Loukas Vyntra opened the scoring after 10 minutes of play, only for Gerard Pique to restore parity shortly after.
Nevertheless, Barca failed to add a second in the remainder of the game as it had to settle for a draw at the Estadio Ciudad de Valencia, much to the frustration of Messi.
"It’s a shame we did not win because we did everything possible to bag the full three points," the Argentine, 26, told reporters. "They closed themselves off at the back and they didn’t give us any space. It’s a difficult stadium to play in, but we tried. We did enough to deserve the win, we just lacked a bit of luck."
Barca remains first in La Liga as second-place Atletico Madrid was held to a 1-1 draw by Sevilla later on Sunday, though Real Madrid's emphatic 5-0 victory over Betis brought Los Blancos within one point of the top spot.