Barca's comfortable hold on the game dramatically fell apart shortly after the interval when Nabil El Zhar headed home a looping cross in the 52nd minute and 20-year-old Oscar Rodriguez turned in a second goal barely 60 seconds later to the joy of the 12,000 fans crammed into the Butarque stadium.
Barca remained top of the standings, however, locked on 13 points with Real Madrid but ahead on goal difference after Julen Lopetegui's side lost 3-0 at Sevilla.
"It's my absolute responsibility, we have four games in 10 days [actually 11] and I thought that Leo and Busquets had to rest knowing that we have a very hard match on Wednesday".
Messi also stated, "You are threatening me, you are threatening me". "We have the strength in depth so we want to make the most of it".
"We did not start well and I was disappointed for my own par in their goal but we did well to take advantage of them switching off".
The Croatian has struggled since his return from a very successful World Cup, with many supporters calling for Arturo Vidal or Arthur Melo to start in his place regularly. Messi came close to scoring the victor with a late free kick, and after the match was shown a yellow card for complaining to the referee.
"We have the squad and the players to be a great team and not depend on anyone, like it always used to be at Barca", Messi added.
Busquets replaced the injured Sergi Roberto early in the second half.
Barca had sporadic chances down the other end, as Suarez struck wide from a free kick and was then thwarted by goalkeeper Unai Simon at point blank range, but Athletic made it third time lucky when De Marcos slid to convert Markel Susaetas cross.
Athletic was trying to win at Camp Nou for the first time since 2001.