Last week's scoreless draw in Tallaght gave Mick Cooke's Drogheda hope of pulling off a Europa League upset against the 19-times Swedish champions, but their chances were shattered by a goal in either half.
A strike from Emil Forsberg on the stroke of half-time gave Malmo the lead and then substitute Simon Kroon netted in injury-time at the end of the game to break Drogheda hearts.
"I think we gave it our best shot. We threw everybody forward from the 85th minute, but to go out on a scoreline of 2-0 is no disgrace," said manager Cooke.
"Malmo are a massive club and they were under great pressure to win, so to go to the 45th minute with the better chances was a great effort. I felt more confident the longer it went on.
"I'm incredibly proud and you want these nights more often, but we either have to win the FAI Cup or improve our league position to realise that ambition. As individuals and collectively, the players showed what they can do."
It was a night that promised so much for Drogheda as they knew that an away goal would have shaken things up and left the team sitting second in the Swedish top flight red-faced.
Plus, there was the carrot dangling of meeting Hibernian in the third qualifying round. But this was always going to be a tough task for Drogheda, no matter how bravely they performed.
However, they did their job of making it tough for their hosts.
Magnus Eriksson and Pontus Jansson had Malmo's best chances in the first half before Forsberg eventually got their opening goal.
A lapse in concentration led to the winger zipping onto Tokelo Rantie's pass and slotting in, but Drogheda were not about to give up and they kept on fighting and making it difficult for their opponents.
On another night, Cooke's men might have profited from a set-piece or a breakaway, but they were ultimately undone when Kroon did well to twist his way into a good position before firing in.
With the goal, Drogheda's adventure came to an end and it is now back to the Airtricity League on Sunday against UCD. But they can certainly be proud of their display.
MALMO – Dahlin; Albornoz, Jansson, Johansson, Ricardinho; Hamad, Halsti, Thern (Friberg 70), Forsberg (Kroon 79); Eriksson, Rantie (Cibicki 87).
DROGHEDA UNITED – Sava; Daly, McNally (Rusk 74), Prendergast, G Brennan; Byrne; O'Conor, O'Neill, Cassidy; O'Brien (Hand 86), Hynes.
Ref – A Abdula (UKR).