Atletico remained second in La Liga, just goal difference behind Barca, after a goalless stalemate in the Spanish capital on Saturday.
Simeone's men had the best chance of the match, but Diego Costa spurned it, as they continued their excellent season with another impressive display.
And the coach was pleased with the effort of his side against Barcelona's array of big-money stars.
"We have a great amount of respect for Barcelona but there is a small difference of some €400million between us," Simeone said.
"We fought – with the weapons we have at our disposal, and that's a good thing.
"With this group of players, who give their lives in every match, we are still able to keep dreaming – taking it game by game."
The draw was the third of the season between the two sides, after their two-legged Supercopa de Espana clash ended at 1-1.
The first leg in Madrid was a 1-1 draw, before another goalless tie saw Barca win on away goals.
Simeone says Barcelona are never at their best against his side, due to the work-rate of their forwards.
"They struggle against us, just as we do against them," he said.
"The secret is down to the hard work our forwards do – without their efforts, it's impossible to function as a team in these sorts of situations.
"Today, we played with a 4-4-2 formation with (David) Villa and Costa working flat out, that shows how committed the team is."