The Bhoys conceded four times in 21 minutes on their return to Seville, with Ange Postecoglou's side losing two goals in quick succession either side of half-time on their way to the Group G defeat.
The visitors deservedly led through Albian Ajeti's goal and a penalty from Josip Juranovic but their opening Europa League group game turned in dramatic fashion just after the half-hour mark.
Juan Miranda pulled one back before Juanmi hit a double either side of a Borja Iglesias goal.
Anthony Ralston headed home with four minutes left but Celtic could not fashion a clear chance to equalise.
The Hoops were missing key players such as captain Callum McGregor, Kyogo Furuhashi, James Forrest, Liel Abada and Greg Taylor, while new striker Georgios Giakoumakis was not ready to feature.
They were also without an away support with hundreds of fans locked outside Estadio Benito Villamarin following a decree by local authorities in the city which hosted tens of thousands of Hoops supporters for the 2003 UEFA Cup final.
But Celtic started on the front foot and Ajeti followed up his weekend double against Ross County to give them a 15th-minute lead and deliver a blow to Betis boss Manuel Pellegrini, who signed him for West Ham two years ago.
There was element of fortune about Ajeti's goal, which was initially ruled out for handball before being overturned by VAR, after an attempted clearance bounced off the striker and into the net.
But the lead was just reward for a brilliant counter-attack featuring moments of skill from Tom Rogic, David Turnbull and winger Jota.
Stand-in skipper Joe Hart also delivered a blow to his former Manchester City boss Pellegrini when he pulled off a one-handed stop from Andres Guardado but Celtic continued to attack with Ajeti, Rogic and Turnbull all threatening.
Ismaila Soro avoided a second yellow card after a late challenge during a Betis break which ended with Hart making a decent stop and the referee further incurred the wrath of the home fans when he awarded Celtic a penalty, although a video check showed there was no doubt.
More good play from Rogic and Turnbull had sent Ajeti through and goalkeeper Claudio Bravo brought him down with a rash challenge.
Stand-in left-back Juranovic produced a confident finish to put Celtic two ahead in the 27th minute.
Jota had the chance to put Celtic three up following a brilliant ball by Turnbull but Bravo made a good stop.
Celtic's lead soon evaporated though with Miranda netting in the 32nd minute after a one-two, moments after hitting the post.
The hosts were level three minutes later after a failed attempt to play offside by Cameron Carter-Vickers. Iglesias squared for Juanmi to knock home.
There were half-chances at either end as the second period began before Betis took the lead in the 51st minute.
With Ralston making his way back from an attack, Soro was slow to cut out a cross and Iglesias got in between Celtic's two centre-backs to flick home at the near post.
Two minutes later, Juanmi ran on to a half-cleared corner, chested the ball down and fired in off the post through a crowd of bodies.
Celtic might have got back into it earlier. Ajeti was denied by an offside flag as he headed home a Rogic cross and the Australian midfielder volleyed against the post.
Turnbull and Ajeti had efforts saved before the former's excellent free-kick was headed home by Ralston from close range, but there was no happy ending for Celtic.