Defending La Liga champions Atletico dropped four points behind leaders and bitter rivals Real Madrid as Barca ran out 3-1 winners.
A week of turmoil was not enough to derail Barca, who raced out to a two-goal lead before half-time thanks to Neymar and Luis Suarez.
Atletico striker Mario Mandzukic reduced the deficit from the penalty spot 12 minutes into the second half before Lionel Messi restored Barca's two-goal advantage three minutes from time.
Simeone praised Barca for their ability to nullify Atletico's threat on the counter-attack.
"Barcelona had a great ability in the first half," Simeone said afterwards. "Good through game, a lot of speed, great intensity, they recovered the ball quickly when they lost it and wouldn't let us go on the counter.
"The rival, which is a very great team, had the ability."
After skewing a ninth-minute shot wide of the post, Messi set up Neymar for the opening goal of the match three minutes later.
Barca continued to dominate the first-half exchanges, though Atletico goalkeeper Miguel Moya was on hand to thwart the hosts.
A stroke of fortune, which saw Messi escape unpunished for an apparent handball, helped Barca extend their lead in the 35th minute, with Suarez netting his second league goal.
Atletico attempted a comeback 12 minutes after the break, Croatia international Mandzukic converting a penalty following a foul on Jesus Gamez.
But the visitors' hopes were dashed with three minutes remaining as Messi converted a cross from Ivan Rakitic.
"It seems there weren’t many chances to score. There weren’t for either, but they were more decisive," said the Argentinean boss.
"In the first and third goal they have many rebounds in favour and they end working out very well. The truth is that the first half was hard for us except for the start, in the first two plays, in which the midfielders and the forwards could play with short passes towards the front.
"In the second half we got in the game. We came close to a draw but the play of the third goal closed the match."
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