A Craig Bellamy strike was only enough to earn Liverpool a 1-1 draw at home to Norwich City on Saturday tea-time.
The No.39 scored at the end of a dominant first half but Grant Holt won the newly promoted Canaries a point with a header on the hour.
Liverpool hit the frame of the goal three times and had a mass of other chances but their day ended in frustration.
The team news saw former Norwich striker Bellamy granted a first Barclays Premier League start since rejoining Liverpool this summer. Steven Gerrard and Charlie Adam made up the midfield in the absence of Lucas Leiva, who missed the match after picking up a fifth yellow card of the season versus Manchester United.
Before those sent out by Kenny Dalglish could attempt to collect another three points, Steve Rotheram MP was introduced to the crowd at the end of a week when his moving House of Commons speech helped ensure there would be full disclosure of all government documents relating to Hillsborough.
The Kop then held aloft a JFT96 mosaic, while opposite them the visiting fans participated in chants of 'Justice'.
Then to the football. Just two minutes had passed when Liverpool threatened the Norwich goal as Martin Skrtel rattled the crossbar with a glancing header from Adam's corner.
Shortly after this Suarez left Leon Barnett dizzy before skewing his shot into the Kop hoardings.
To say Norwich's defending was haphazard in the opening stages would be kind, but there was little they could do to contend with the quality displayed on 11 minutes when Adam launched a pinpoint pass to Bellamy on the left. The Welshman's cross was directed first time onto the woodwork by Suarez before Downing failed to capitalise on the rebound.
Liverpool's passing was reminiscent of a pinball machine at times and it produced another excellent opportunity for Suarez on 17 minutes - but again the Uruguayan fired wide.
At the other end Norwich almost took an unlikely lead when captain Wesley Hoolahan forced a close range save from Pepe Reina, and the opening gave them a belief that had been lacking up until then.
Still, Liverpool seemed the more likely, and a spill by John Ruddy would have led to an opener had Suarez found the unmarked Dirk Kuyt in front of goal.
Downing then crossed from his position on the right but Suarez could not generate enough power to head beyond Ruddy.
The goal finally arrived in first-half stoppage time when Russell Martin fell over under pressure from Suarez, allowing Bellamy to steam through on goal and finish via a deflection.
Anthony Pilkington blasted low and hard towards Reina immediately after the restart but the Spaniard never looked troubled.
Liverpool were then denied by the woodwork for the third time when Suarez waltzed past Barnett before seeing his poke deflected onto the post. The 24-year-old was everywhere, pestering and probing without getting his name on the scoresheet.
He and Liverpool could have had several, but instead Norwich were still in the game, and their hopes of gaining a result at one of English football's most famous arenas were about to get a whole lot more realistic on 60 minutes when substitute Holt nodded in a Pilkington cross at the Kop end. Game on.
Liverpool surged to restore order, Suarez again breaking loose only to be thwarted by a palm away from the goalkeeper.
Henderson and Carroll were introduced as Dalglish tried to influence proceedings, but it was that man Suarez who seemed most likely to change the game. He was again unlucky to come up against an in-form Ruddy after Barnett fell to the ground.
Carroll headed narrowly wide and Suarez had a volley tipped away in stoppage time but the day ended in disappointment for those in Red.
Liverpoolfc.tv journalists' man of the match: Luis Suarez.