Barca's first loss, a 2-1 defeat at Ajax in the Champions League last Tuesday, saw their 20-match unbeaten run under new coach Gerardo Martino come to an end - one short of matching the club's best-ever start to a season.
And there was more disappointment for the reigning Spanish champions on Sunday as they slumped to a 1-0 league defeat at the hands of Athletic.
That result means Barca now only lead La Liga on goal difference from Atletico Madrid, while improving Real Madrid are just three points back having won their last five league games.
Nevertheless, Spain international Busquets is refusing to get overly concerned by their recent results, saying after the Athletic defeat: "There's no need to be alarmed, we just have to carry on.
"We have to win the two (league) games that are left to play this year and learn both from our errors and the things we are doing well."
Athletic took all three points against the champions thanks to Iker Muniain's goal 20 minutes from full-time.
It was no more than the Basque giants deserved as they continued their impressive start to life at their new stadium, which has seen them win six and draw the other two of their eight games.
Barca midfielder Andres Iniesta felt his side were relatively comfortable until the goal, saying on his club's website: "We had the game under control, but the goal really hurt us. San Mames is always a tough place to come to.
"We put in a good first half and we played well at times after the break, but the goal really shook us and although we really tried, we couldn't come back."
Javier Mascherano added: "Nobody likes to lose, the defeat hurts, but let's not forget we are still leaders
"We're going away sad. We were more intense than against Ajax, but that wasn't enough to give us the win.
"We have to put right the things we have done badly and we must be self-critical, but we've done things well too.
"We have to win the games that are left this year, beginning with the matches against Cartagena and Villarreal."
Barca, whose star forward Lionel Messi is sidelined through injury and is unlikely to be available again until the new year, are next in action against third-tier Cartagena on Friday in the first leg of the Copa del Rey last-32 tie.