Few could have anticipated such a slapstick performance at the back from Barca, who conceded four goals at Camp Nou for the first time since April 2003.
Junior Firpo and Joaquin had put Betis two up at the interval before Messi sparked hopes of a comeback from the spot.
Valverde also confirmed goalkeeper Marc-Andre ter Stegen is fine to play, despite having been omitted from Germany's squad for the upcoming worldwide window to rest a minor shoulder injury.
"We have been a courageous team in every way", former Spain global Joaquin said.
Barca reduced their deficit in the 68th minute through a Lionel Messi's penalty kick, but three minutes later Giovani Lo Celso increased his side's lead. "Winning at the Camp Nou requires concentration and doing everything very well".
"We understand that any player theoretically can play the game, but of course there is always a period where you need to be careful", he said.
Arturo Vidal quickly responded with a goal down the other end but Rakitic was then dismissed for a second booking and Sergio Canales soon made it 4-2. He weaved inside Sergi Roberto and found the net.
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He also delivered a stinging indictment of nationalism , calling it "the exact opposite" of the patriotism shown by soldiers. At the forum German Chancellor Angela Merkel warned against taking peace for granted, saying, "We have to work for it".
His playing time has been limited by a series of hamstring injuries and after falling foul of the club's disciplinary code, including turning up late for a team meeting before the game with Inter in October. Betis forced ter Stegen to come off his line and make a smothering save near the left post, which he did before booting the chance clear.
Vidal replaced the jaded Arthur Melo at half-time and shot within a minute of the restart.
The home side predictably started the second half in determined fashion and Messi and Luis Suarez both shot wide before they were gifted a lifeline as Tello was penalised for pulling back Jordi Alba as he tried to drive into the area.
Coach Quique Setién's men doubled their lead through Joaquín in the 37th minute with Cristian Tello setting up the goal the away team.
Ivan Rakitic was sent off for the Catalans in a calamitous defensive showing. Brais Mendez scored a second for Celta in injury-time.
Messi's second goal of the afternoon was initially ruled out for offside before the decision was overturned by the VAR, but Betis held on for a famous victory.