The Argentina international feels the Blaugrana did enough to emerge victorious and has rued their lack of fortune
The Catalans fell behind early on 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 they 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 remain first in La Liga as second-placed Atletico Madrid were held to a 1-1 draw by Sevilla later on Sunday, though Real Madrid's emphatic 5-0 victory over Betis brought them within one point of top spot.