The Argentinian was appointed after Betis sacked Juan Carlos Garrido this week in a bid to improve the fortunes of a team which had collected just 11 points from their opening 20 fixtures in La Liga.
His tenure had looked set to get off to a positive start when Ruben Castro gave the visitors the lead in the 17th minute, but two goals from Fabian Orellana and one from Charles turned the match on its head before half-time.
Substitute Nolito added a fourth goal for the hosts 17 minutes from time and, although Ruben's second of the game made the scoreline more respectable, it was too little, too late.
It all started brightly enough for Calderon's team, Ruben despatching a left-footed shot home from close range from Juanfran's right-wing cross.
The lead lasted only five minutes, though, before Orellana headed Rafinha's cross past Guillermo Sara.
Charles made it 2-1 just after the half hour mark when he nodded a Hugo Mallo centre into the net.
Sara had to be alert to keep his side only one goal down soon after, tipping another Charles header - this time from an Orellana corner - away to safety, but it was not long before the home fans were celebrating goal number three.
Charles this time turned provider, setting up Orellana for a clinical right-footed finish into the top-right corner.
Luis Enrique's side pulled further clear in the 73rd minute when Nolito met Charles' right-wing cross with a volley which had the beating of Sara.
Ruben got it back to a two-goal deficit five minutes later by diverting Salva Sevilla's free-kick past Celta goalkeeper Yoel, but the visitors could make no further inroads.