Lamine Yamal opened the scoring at the Olympic Stadium but, in another performance marked by comical defending, Barça found themselves 2-1 and 3-2 down against second-bottom Granada.
Yamal's second goal of the night earned Barça a point but the 16-year-old's brace could not prevent the Catalan side dropping two more points in the title race.
"LaLiga was already difficult and now even more so with more points gone," Xavi said in the post-game news conference.
"It's a big gap to Madrid and five now to [second placed] Girona, but we are not going to throw the towel in.
"What we have to do is not slip up anymore. We had chances to kill the game and I think we have gifted Granada goals when there was little danger. The team had faith, courage and desire, but it wasn't enough. It makes things even more difficult."
Barça's season has been underpinned by bad defending. Ricard Sánchez and Facundo Pellestri gave Granada the lead, with Robert Lewandowski levelling before Ignasi Miquel restore the visitor's advantage.
This was the second time in a month the Blaugrana have scored three at home and failed to win after losing 5-3 to Villarreal in January.
They have now conceded 24 goals in 11 games in all competitions in 2024, more than any other side in Europe's top five leagues.
"We gave away too much defensively," Xavi added. "We conceded three goals against Villarreal; then again today. That makes it difficult to win anything.
"We have to minimise the amount of mistakes. It's the same defensive errors that have marked the season. It was the same in the draw at Granada earlier in the campaign."
Barça's strength as they won the title last season was their defence. After 24 league games, they had conceded just eight times. They have leaked 33 at the same stage of this campaign.
"It's sport," Xavi said when asked to address the difference. "Form changes, a loss of players, players that have not been able to play together ... concentration errors.
"We have done a lot of good things to win many games, but these mistakes in defence are the difference in points between us and Madrid and Girona."
After that defeat to Villarreal, Xavi announced he will step down at the end of the season. He said the Granada result was a "step back" but suggested a run of seven points from nine since his decision showed there has been a reaction from his players.
Meanwhile, Yamal continues to grow into one of the team's key players despite his inexperience. His double against Granada took him to three LaLiga goals, a tally never previously reached by someone before their 17th birthday.
Granada coach Alexander Medina said they had done work to stop the Spain international but were unable to execute their plan.
"He's a kid with an enormous present and future in the game," Medina said in a news conference. "When we analysed Barça this week, he was one of the strong points we had to try and stop.
"We proposed double marking, extra coverage ... but football is a beautiful game and in the end it's the players who define games, beyond any strategy, and a kid of 16 years old has shown us that with two goals and an impact on the game that, as much as we had planned to try and control him this week, we couldn't stop.
"He has an immense present and future and a lot more to give and to grow."