The champions moved third, a point clear of Atletico Madrid, but trail Real Madrid by four and surprise leaders Girona by six, having played one game more than all three sides.
Atletico fell 2-0 at Athletic Bilbao earlier Saturday but the Catalans could not take full advantage in an entertaining clash on the east coast.
Joao Felix sent Barcelona ahead in the second half after a slick team move, but Hugo Guillamon's fine strike pegged them back.
"We have to be much stronger in the opponent's box, the chances are so clear (and) we didn't win the game," Xavi told Movistar.
"I think we gave away two points, because the team had a very good game... we take away a point that leaves us very unsatisfied."
Barcelona have won just one of their last four league matches, including being ripped apart by a rampant Girona last weekend at home.
They were further shaken by a midweek Champions League defeat by Belgian side Royal Antwerp, which created further questions over Xavi's management even though the Catalans were already through to the last 16.
In the subsequent days, club figures, including president Joan Laporta, showed him support, ahead of what Spanish media billed a 'final' at Valencia's rowdy Mestalla stadium.
"Anything that wasn't three points was a tough blow for us," Barca midfielder Pedri told Movistar.
"We did a lot of things right but we didn't get the goal -- I think our play was a lot better than in the Girona game, where we weren't good."
The Spain international said the team were backing Xavi.
"We're with the coach, these aren't good moments for any of us... we have to be united to turn it around."
As in Barca's defeat by Girona, the game flowed from end-to-end.
Both goalkeepers were called into action before Felix sent Barca ahead early in the second half.
Frenkie de Jong played in Raphinha with a delightful pass and the Brazilian teed the ball up for the Portuguese forward to tap home.
Guillamon equalised in the 70th minute after Barcelona defender Ronald Araujo allowed a ball to bounce instead of clearing his lines.
The Spain midfielder found the top corner from the edge of the box to put Ruben Baraja's team level. Ferran Torres and Raphinha missed big chances in the final stages as Barca searched for a winner.
The draw takes Valencia 10th, with Baraja's side significantly more solid than last season when they battled relegation.
Leaders Girona host Alaves on Monday, after Real Madrid welcome Villarreal on Sunday.
Lions roar
Athletic Bilbao powered to a convincing 2-0 victory over a flat Atletico Madrid on Saturday in La Liga to close the gap on the top four.
Gorka Guruzeta and Nico Williams struck second-half goals to deservedly secure the points for Los Leones, who dominated at a jubilant San Mames.
Atletico have lost four games in La Liga this season, each away from home, while winning all eight matches they have played at their Metropolitano stadium.
"We cannot play like this, one way at home, another away, you can't win titles like this, you can't win leagues," Atletico goalkeeper Jan Oblak told Movistar.
Ernesto Valverde's Athletic tested Oblak frequently, with brothers Inaki and Nico Williams both striking the woodwork, while Oihan Sancet skied a penalty.
Inaki Williams, making his 400th appearance for Athletic, helped create the opener, finished by Guruzeta from Ander Herrera's cross.
Nico Williams added a stunning second when he bent a shot over Oblak into the far top corner with his weaker left foot.
Despite defeat and his team's drab display, Atletico coach Simeone maintained a positive attitude.
"Today is the day I am calmest," he told reporters.
"I know the boys are giving me (everything) and I am with them to the death."
Struggling Sevilla, 16th, fell to a humiliating 3-0 home defeat by Getafe and then sacked coach Diego Alonso.
The Uruguayan failed to win a single match from 12 in either La Liga or the Champions League since being appointed in October.
