Well headed into the second leg as firm underdogs looking to overturn a two-goal deficit against their Greek opponents although they survived an early onslaught to go in goalless at the interval.
Yet Lazaros Christodoulopoulos and Charalampos Mavrias, both of whom scored in the first leg, put the tie beyond any reasonable doubt after half-time before Ibrahim Sissoko sealed an emphatic victory.
The Scottish side acquitted themselves well last week but were left with a mountain to climb with Panathinaikos scoring a soft early goal and a late second on the counter-attack. Panathinaikos looked to consolidate their advantage in the early running and Motherwell could have found themselves two further goals down in the first five minutes.
Jose Toche's 25-yard strike forced goalkeeper Darren Randolph to parry away while the 29-year-old Spaniard should have done better moments later after going through on goal but he could only shoot wide of the right-hand post. It was a let-off for the visitors but there was little respite as the Greek side continued to control the tempo of the match.
Nicky Law nearly gave McCall's men a glimmer of hope against the run of play but his fierce effort from just outside the area was pushed away by Pana keeper Orestis Karnezis. It was a rare moment of attacking intent from the Steelmen, who started to force their way back into the contest.
But while they were seeing plenty of the ball, their opponents seemed content to sit on the back foot and Keith Lasley's optimistic long-range strike that sailed over the bar was their only other sniff at goal before half-time. Motherwell's luck was finally up as Christodoulopoulos put Panathinaikos ahead on the night and the tie seemingly beyond doubt.
There seemed to be little danger when Shaun Hutchinson fouled Sissoko 35 yards from goal but striker Christodoulopoulos, who also scored the opener at Fir Park, magnificently fired into the top corner and past a despairing Randolph in the 51st minute.
Panathinaikos continued to push forward and they had a claim for a penalty waved away despite the ball seemingly striking Cummins on the arm. The one-way traffic continued and Mavrias - scorer of Panathinaikos' second goal last week - extended their lead on the night in the 75th minute by dribbling past the defence and comfortably shooting past Randolph.
Motherwell's miserable night in the Greek capital was completed eight minutes later. After they were dispossessed deep in Panathinaikos' half, Kostas Katsouranis broke down the right for the hosts and his cross into the centre was slotted home by Sissoko.
Basel managed a 1-1 draw at home to Molde, qualifying 2-1 on aggregate, after Ole Gunnar Solskjaer's Norwegian champions missed a penalty in the second minute of stoppage time which would have sent them through.
Magne Hoseth's effort was saved by Yann Sommer in the third qualifying round, second leg tie.
Earlier, Jo Inge Berget had given Molde a first-half lead against nervy Basel who levelled through David Degen with 15 minutes left.
AEL Limassol's attempt to emulate fellow Cypriots APOEL Nicosia, who last year made the quarter-finals, continued as a 1-0 win at Partizan Belgrade gave them a 2-0 aggregate victory.
Dosa Junior scored the winner for Limassol's cosmopolitan line-up, which included players from Angola, Portugal, Brazil, France, Argentina, Ivory Coast and one from Cyprus itself.
Caner Erkin opened the scoring for Fenerbahce and Marius Nikulae replied for Vaslui in a clash between two non-champion teams.
Second half goals by Joe Ledley and Giorgos Samaras gave Scottish champions Celtic, the 1967 winners, a 2-0 victory at HJK Helsinki for a 4-1 aggregate success despite Victor Wanyama being sent off for a second bookable offence after the break.
Christian Bolanos and Cesar Santin scored in the last 15 minutes to give FC Copenhagen a 3-2 win at 1978 runners-up Bruges which took them through and Thomas Sorum's hat-trick gave Helsingborg a 3-1 win over Poland's Slask Wroclaw.
The Swedish champions qualified 6-1 on aggregate.
Luxemburg champions F91 Dudelange's dream run ended with a 1-0 defeat at home to Maribor. Dudelange, beaten 5-1 on aggregate, had knocked out Salzburg in the previous round.
Among the other clashes, Dinamo Zagreb thrashed Moldova's Sheriff Tiraspol 4-0 to go through 5-0 on aggregate and Anderlecht beat Lithuania's Ekranas Panevezys 6-0 to complete an 11-0 aggregate victory.