Barcelona threw away a three-goal half-time lead on the day Xavi was appointed coach as Celta Vigo scored in the 96th minute to complete a stunning comeback in La Liga on Saturday.
Barca produced one of their best displays in the first half and took a 3-0 lead into half time thanks to goals from Ansu Fati, Sergio Busquets and Memphis Depay.
But their good work was undone after the break and a goal from Nolito and two from Iago Aspas pulled off a tremendous comeback for Celta.
"I think in the second half we forgot to play, we were very passive and we lacked character," Dutchman De Jong said.
"This was a very important game for us to climb a little higher in the table and the result is a very big blow for us."
Xavi has two weeks to prepare for his first game in charge against city rivals Espanyol after ending a six-year spell as player and then coach with Qatari side Al Sadd to return to Barca, where he played 767 games and won eight La Liga titles as well as four Champions League crowns.
It is now Xavi's job to pick Barca up, with the team's new coach watching the match on television in the city having landed around three hours before kick off.
"We'll have to see how it goes, the fans are very excited about it and the players are going to work very hard," added De Jong.
As well as a galling result which left the team without a league win in four games, Barca lost Eric Garcia, Fati and Nico to injury, leaving them with a total of 11 players out of action.
Caretaker coach Sergi Barjuan said the team urgently needed to look at the problem.
"It's very strange and it would be good to find out why and ensure it doesn't keep happening," he said.
"We have a lot of problems with injuries and while it isn't an excuse, it's very important for the future.
"If you look at the line-up, you're playing kids. We were relying on kids. With everyone, we are stronger."
Real Madrid increased the gap between Barcelona and the top of the standings to 10 points after beating Rayo Vallecano 2-1.