The European champions saw their lead at the top of La Liga shrink to three points over Atletico Madrid with six games remaining after they beat Espanyol 3-1.
Real Madrid are also in the title race a point further adrift as they saw off Basque minnows Eibar 4-0.
“We have never said the league is over,” said Enrique.
“It is a marvellous opportunity to show we are the best team in the world and that is why we carry that badge on our chest.”
Barca have taken just one point from their last three league games to see a commanding lead slip away, but they still need to drop points in two of their remaining matches to surrender top spot, thanks to their better head-to-head record with Atletico.
Defeat also continued Barca's miserable run at Sociedad's Anoeta stadium, where they have now lost on their last four league visits.
“Evidently, there is a title race with six games remaining. It is an exciting and open league which the best team will win. At the moment we are top,” added Enrique.
Barca also face a huge challenge to maintain their hopes of becoming the first side to retain the Champions League when they visit Atletico for their quarter-final, second leg on Wednesday.
The Catalans travel to Madrid with a 2-1 lead handed to them by Luis Suarez's double after Atletico had been reduced to 10 men by Fernando Torres's first-half red card in the first leg.
“Pessimistic thoughts and opinions that I'm sure will accompany us in the coming days don't benefit the team at all,” Enrique continued.
“We are not machines, we are human. Evidently, today is not a good day for us, but we have to lift ourselves from the moment we leave this beautiful stadium which doesn't bring us much luck and think that on Wednesday we have the chance to be in the semi-finals of the Champions League.”
As well as missing the suspended Suarez, Enrique had left Andres Iniesta, Ivan Rakitic and Jordi Alba on the bench with one eye on the visit to the Vicente Calderon.
All three were called into action after the break, but Iniesta and Lionel Messi were both twice denied by Sociedad keeper Geronimo Rulli.
“In the first half we didn't create enough chances,” said Iniesta.
“In the second half we were better, but we didn't take our opportunities.
“Everything is getting tighter at the top and we've used up the cushion we had, but we are still Barcelona and we are still close to our objectives.”
Meanwhile, Barca defender Gerard Pique called for a big reaction from his teammates to ensure their Champions League dream isn't snuffed out by Atletico.
“The important game is on Wednesday. That is when we have the most important competition at stake.
“No team can do everything perfectly all season. We know what we have to improve on.”