Depor began the game 17th in the standings while Barcelona, who had won 8-0 at Riazor last year, were looking to tighten their grip on top spot but instead lost for the first time in the league since they were beaten at Celta Vigo on Oct. 2.
"Only someone who has lived what we lived this week can understand what it means but professionals need to know how to cope with these situations," Enrique told reporters.
"We knew it would be difficult here but what happens before a game always has an impact in the next. It's better to arrive at a game feeling euphoric than pessimistic, we were focused, but we still lost."
Barca were knocked off from the top of the standings by Real Madrid after Zinedine Zidane's side beat Real Betis 2-1 in Sunday's late game.
Enrique said he was disappointed his side could not build on the momentum gained from winning five games in a row and scoring 17 goals in their previous three.
"We lacked clarity in the final few metres and it's a shame because this game was crucial to keep our confidence high and for our rivals to see that we mean business," he added.
"We didn't have the fluidity we needed to overcome their deep defending. They grew in confidence and we made errors. [Sunday] it was crucial that we scored first but they did. We have to accept this defeat and remember there's a lot of games left."
Barca defender Gerard Pique added the comeback against PSG, where they overcame a 4-0 first leg defeat, had taken its toll.
"Sport is like this, we aren't machines and after the effort we made on Wednesday it was very difficult to compete again. We have to congratulate Deportivo, they were the deserved winners of this game," he said.
Pique also tried to put the week in perspective.
"Every Barca fan would have signed up to coming back against PSG and then losing in Coruna," he added.
"We'll continue to fight for the league title until the end. There's still a long way to go and we'll have chances to win it."