Two set-pieces proved Derry City's downfall as their Uefa Cup dream ended away to Paris St Germain.
PSG's Kalou is beaten to a high ball by Derry's Eddie McCallion
Stephen Kenny's men, who had held PSG 0-0 in the first leg, were soon in trouble as Edouard Cisse headed in from a corner after just six minutes.
Pedro Pauleta made it 2-0 four minutes before half-time with a low shot after Paulo Cesar had pulled back a free-kick on the right wing.
Late on Derry defender Darren Kelly cleared off the line from Rodriguez.
After the goalless first game, the Candystripes felt they had a chance of becoming the first Irish side to reach the group stages of a major European competition.
But that Cisse opener dashed the plan to keep things tight early on.
Cisse's downward header ended up in the roof of the net after Derry's Barry Molloy and keeper David Forde got in each other's way.
And the Eircom League side's defence was found wanting again when the free-kick move caught them out and Pauleta's side-foot found the net on 41 minutes.
Ken Oman had a rare shot for Derry that flew over the bar, while PSG substitute Rodriguez sent a stoppage-time chance wide of the target.
"Tonight was a bridge too far but we must keep on trying to improve as a team," said City boss Kenny.
"PSG are a step-up - they are France's biggest club - and we did all right.
"But conceding that first goal from a set-piece was devastating. Then having to get two was ambitious because we did not really threaten the PSG goal."
PSG: Landreau, Rozehnal, Mendy, Paulo Cesar, Traore, Armand, Drame, Cisse, Frau, Pauleta, Kalou.
Subs: Alonzo, Diane, Yepes, Pancrate, Chantome, Rodriguez, Hellebuyck.
Derry City: Forde, McCallion, Kelly, Oman, Hargan, Molloy, Deery, Martyn, McCourt, Brennan, Beckett.
Subs: Jennings, Hutton, Higgins, McHugh, McGlynn, Farren, O'Flynn.
Referee: Oleh Oriekhov (Ukraine)