Despite their their lack of European experience the Reds were overwhelming favourites to progress. Even the Reykjavik chairman thought so.
"A loss like 5-0 would even be impressive for us," admitted Mr Sirurger Gudmannsson. "We certainly do not expect to win but we will fight and try to defend our goal with all the power we can muster. What is of the greatest importance for us is have such a famous and fine team like Liverpool visit Iceland."
Bill Shankly did not have the opportunity to see Reykjavik play before the tie but he refused to underestimate them and made sure that he spoke to many people who had played against them.
For everyone in the Liverpool squad it was to be a new experience and 24 hours after a 2-2 draw at Anfield against West Ham in the Charity Shield, they set off for Iceland.
"Most of us didn't even know where Reykjavik was," recalls the then captain Ron Yeats. "We flew from Manchester to London, then from London to Prestwick in Scotland and finally caught a flight from there to Iceland. When we got to Scotland, we had four or five hours to kill, so Bill Shankly decided to take us to the Butlins holiday camp in Ayr.
"When we got there Shanks said to the manon the gate, 'We are Liverpool Football Club, on our way to play a European tie in Iceland.' The fella just looked at him and replied, 'Oh aye, well you're on the wrong road here mate!'"
Bright sunshine and bitterly cold temperatures greeted the Reds party when they finally arrived in Iceland but they quickly adapted and set about their task in a typically professional manner.
The Icelandic champions set their stall out to defend from the start in the hope of keeping the score respectable but within three minutes their best-laid plans backfired on them. Roger Hunt crossed from the right and Gordon Wallace rifled home to open the scoring.
Liverpool were far superior in all departments and their part-time hosts were totally outclassed. Peter Thompson was the main protagonist, weaving his way through the Reykjavik defence like a hot knife through butter.
Tommy Lawrence in the Reds goal was a mere spectator but it took until a minute after the restart before Liverpool increased their advantage. Wallace had a shot blocked and Roger Hunt was on hand to convert the rebound.
In the 52nd minute the hosts forced their first corner of the match but it was only a brief respite from the Liverpool onslaught. Four minutes later a Callaghan centre was pushed out by the Reykjavik keeper, the ball fell straight to Phil Chisnall and he found the back of the net to make it 3-0.
Wallace scored his fourth goal in two games with a header on 63 minutes and two minutes from time Hunt completed the rout. Afterwards the Reykjavik players were unanimous in their praise of the Reds, with many rating them the best side to ever visit Iceland.
Reykjavik: Guddjonsson, Arsaelsson, B Felixson, T Jonsson, H Felixson, Kjartansson, Gudmundsson, S Jonsson, G Felixson, Schram, Gudmannsson.
Referee: Mr A Van Leeuwen (Holland)
The return leg at Anfield was a mere formality but nevertheless a crowd of over 32,000 turned up to witness the historic occasion that was Liverpool's first European home tie.
The Reykjavik squad arrived in Liverpool on the previous Saturday. They trained at Melwood the following afternoon and on the day of the game their players and officials were treated to a civic reception at Liverpool Town Hall.
That was where the goodwill of the hosts ended. Out on the pitch Liverpool emphatically confirmed their passage into the next round with a thoroughly professional performance.
Gerry Byrne opened the scoring on 13 minutes with a shot from 35-yards and Ian St John (pictured left), back in the side after an appendix operation, extended the lead ten minutes later.
The sporting spirit that was so evident in Iceland was repeated at Anfield - so much so that the fans on the Kop began chanting for the visitors. Indeed, the biggest cheer of the night was when Felixson scored a consolation goal for Reykjavik in front of the Kop after 35 minutes.
As a contest, the game was nothing more than a gentle stroll in the park for the English Champions and they quickly recovered from the shock of conceding that goal by restoring their lead through Roger Hunt shortly after half-time.
Bobby Graham, a replacement for the injured Gordon Wallace, made it 4-1, heading home from a precision cross by A'Court, in his final first team game for the club, and two minutes later Willie Stevenson heaped further misery on the Icelander's by hammering home a fifth.
An 11-1 aggregate win was completed 16 minutes from time when St John grabbed his second of the night. The visitors were well beaten but their plucky performance earned them a standing ovation from all parts of the ground and the Liverpool players even joined in theapplause, forming a guard of honour as Reykjavik left the field.
Afterwards players and officials of both clubs enjoyed a meal together at the Adelphi Hotel in Liverpool city centre and before returning home Reykjavik announced their wish to see the Reds go on and win the European Cup.
Liverpool's introduction to European competition could not have been more pleasant.
Footnote: On August 12, 1984 Liverpool and Reykjavik met a pre-season friendly to commemorate the 20th anniversary of this tie.