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But after Jose Gimenez's excellent 18th-minute header was cancelled out by an Anton Miranchuk penalty seven minutes later, Atletico were unable to find another goal despite having a host of opportunities.
Simeone's Atletico hit the crossbar twice, had a goal disallowed, and Lokomotiv goalkeeperGuilherme was outstanding, the captain leading his Russian team by example.
Atletico's overall performance delighted boss Simeone, who has twice led Atletico to Champions League finals.
"I leave with a very good image of the team," Simeone said.
"The Lokomotiv goalkeeper had a great performance, he took very important balls.We were very good against a team who defendvery well and counter-attackvery well, as was seen against Bayern and Salzburg.
"It's a pitywe did not have the forcefulness ongoal but I think this is the way to go to win games."
Atletico played an entertaining game, catching the eye as they went forward andcreateda stack of chances, with Luis Suarez and Joao Felix both going close.
Koke's header and Angel Correa's 20-yard strike hit the Lokomotiv bar, but a winning goal would not come.
Suarez put the ball in the net after Koke rattled the Lokomotiv goal frame, but he had stepped offside.
Atletico attempted 27 crosses in the game from open play, with right-back Kieran Trippier responsible for eight of those.
The England defender got forward regularly and had his delivery been a touch more accurate at times, Atletico may have cashed in.
Captain Koke agreed with his coach that Atletico went about the game in the right way.
"It was a game where we wereunlucky. We cannot regret it, we have to keep going," Koke said via Marca.
"The team made a great effort to try to take the three points, but it wasn't to be. We had chances: the bar, the goalkeeper, the disallowed goal... we just have to continue, we are doing a great job."
Atletico are unbeaten after six games in LaLiga this season, and they have come back strongly in the Champions League after a 4-0 defeat to titleholders Bayern Munich in their opening Group A game.
Victory over Salzburg in their second group game could easily have been followed by another three points on Tuesday.