The team often described as the best in the world had drawn with Sporting Gijon and lost to Arsenal in the Champions League and when Bilbao's Andoni Iraola levelled with a second-half penalty at the Nou Camp, they were clearly rattled.
With Real Madrid having narrowed their lead at the top to two points with a comfortable 2-0 win over Levante on Saturday, Barca were uncharacteristically rushed as they poured forward looking for the winner.
"We couldn't allow ourselves another slip up because Madrid were close. Every game is vital," Messi told Spanish television.
"Bilbao were very organised in the way they put us under pressure and played very well. These are three important points."
Fourth-placed Villarreal's faltering form continued when they were held 1-1 at home by basement side Malaga and Osasuna's new coach Jose Luis Mendilibar led his team to a stunning 4-0 win over sixth-placed Espanyol.
Barca's 16-match winning streak in the league ended with a 1-1 draw at Sporting last weekend and a 2-1 defeat at Arsenal in the Champions League on Wednesday suggested the Spanish champions were suffering a dip in form.
Those doubts appeared misplaced when Xavi's diagonal pass over the defence found the overlapping Dani Alves who cushioned a volley inside for Villa to fire first time into the corner after only four minutes.
For all their domination, however, they could not find a second and when Sergio Busquets brought down Fernando Llorente for a penalty, Iraola's 49th-minute spot kick increased the tension in the stadium.
"It makes me laugh when people say Barca are in crisis," Bilbao coach Joaquin Caparros told reporters. "In my view, it was the same Barca as ever."
