Atletico will return to Madrid for the second-leg of the quarterfinal in confident mood.
The visitors survived the loss of their top-scorer Diego Costa, who left the pitch when the game was just half an hour old with a hamstring injury, to take the lead 11 minutes into the second half when the forward's replacement Diego Ribas unleashed a rasping drive into the top corner.
Neymar equalised for the Catalans in the 71st minute and from then on Atletico were hanging on, with goalkeeper Thibaut Courtois making three vital saves from Sergio Busquets, Andres Iniesta and Lionel Messi before the final whistle sounded.
"I'm very happy with this team, this was the most decisive game of the two years I've been at the club and we are still going, showing enormous heart, and the way we fought makes me so proud, and I'm sure the fans are proud too," Simeone told the post-match press conference.
"I'm delighted we were able to compete with Barcelona, you don't earn the right to do that in a day, you earn it with hard work and today we showed we can compete with them."
The coach admitted Atleti were made to suffer in the final 20 minutes, but added: "This is the history of Atletico Madrid, always suffering, playing with their heart, never giving up, always keeping going.
"This group of players has huge heart. More than the result, here or in the return leg, this is what makes me proud."
On Diego's goal, Barca coach Gerardo Martino joked: "When I saw the ball go in I almost wanted to celebrate it, it was a tremendous goal."
The Argentinian also insisted he was pleased with his team's performance.
"The way Barca played fills me with pride," he said. "Sometimes it paid off, other times it didn't, but if we keep playing this way we will have every chance of success.
"I'm very happy with how we played, we deserved to score another goal. We maintained intensity over the 90 minutes and we didn't allow Atleti to play in space, we created more chances and their only chances came from a bad pass and a goal from 35 metres."
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