Brazilian forward Diego Ribas, who had come on to replace Atletico's injured talisman Diego Costa after half an hour, put the visitors ahead on 57 minutes when he unleashed an unstoppable drive.
But Barcelona drew level 14 minutes later when compatriot Neymar converted a fine pass from Andres Iniesta.
The hosts finished the game strongly, with Atletico goalkeeper Thibaut Courtois making outstanding saves, denying first Iniesta and then Lionel Messi as the visitors held on to earn a fourth successive draw in the meetings between the two teams this season.
The latest stalemate leaves both with everything to play for in next week's return leg at the Vicente Calderon.
Martino told UEFA's official website: "I am full of pride in the way in which we played. If we continue like this, there are chances for success.
"Our intention in every game is to go out and win, so we will have to go (in the second leg) and do what we always try to do.
"After (the opening) goal you saw the best of Barcelona. In the second half we moved the ball about well and played with depth. There were also good moves in the final third and several shots. We played as a team and added a lot of intensity."
He added: "The tie is finely balanced. I do not know if the factor of playing at home second counts for anything, but like I said, everything is evenly balanced."
Barca were forced into an early change when defender Gerard Pique was left injured following an aerial challenge and he was replaced by Marc Bartra, with the Spain international now facing four weeks on the sidelines.
Opposite number Diego Simeone was pleased with his side's performance and also that Diego got on the score-sheet, while he is hoping for the best as regards Diego Costa.
He said: "I am really happy for Diego and for the goal he scored tonight. He needed that. He came on in a very important moment in the game. He will be fundamental for us from now until the end of the season.
"Diego Costa did not want to come off the pitch. We will see what he has tomorrow - we are hoping for the best.
"Tonight we played against a great rival. We have a team with huge heart and it made me so happy to be able to compete against these opponents.
"It was a passionate affair. From a tactical point of view, it was a beautiful game. Both teams played to their strengths and stayed true to their style. The Vicente Calderon will be bursting with atmosphere (for the return leg)."