The midfielder scrambled in a 94th-minute winner from close range to see Barca to their victory at the Mestalla.
Busquets, who netted after Neymar's header was kept out by Diego Alves, said Luis Enrique's men were lucky to get their late chance.
"We were very fortunate to get that chance in the last minute. It makes us feel delighted after a very hard struggle," Busquets told television reporters.
"We knew it was going to be difficult and it certainly was, but we kept fighting until the end."
The goal was Busquets' first in La Liga since September 2013, when he struck against Real Sociedad.
Barca's win lifted them to within two points of leaders Real Madrid, and Busquets said it was an important victory.
"In this league you could say a draw is never a good result," he said.
"But obviously at the end of the day when you come here and attack as much as we have done in the closing minute.
"Diego made an amazing save against Neymar and fortunately the ball fell for me and I was able to put it into the back of the net."
