Amid the elation of Brendan Rodgers' first league win as Liverpool manager there was cause for concern. Luis Suárez scored a hat-trick but should, not for the first time this season, also have had a penalty after being bundled over by Norwich City's Leon Barnett.

Liverpool's subsequent ruthlessness in front of goal reduced the incident to no more than a footnote as far as the result was concerned, but the issue has the potential for a wider resonance. Rodgers, who spoke to Mike Riley, head of the Professional Game Match Officials, last week to outline his concerns about refereeing performances, admitted he is concerned that Suárez's reputation may be influencing officials.

"There is that fear," he said. "There are players, attacking players who go down at times. I could tell you about three or four strikers who go down in the box with very minimal contact and all of them have had penalties this year.

"I can't worry too much about it. It's something that hopefully the referees, when they analyse and assess their own performance, they have a look at it. We just have to concentrate on building our game, developing our football, and hopefully these penalties that we don't get won't come back to haunt us."

Officiating has been a bugbear for Liverpool and Suárez this campaign, but if they continue to perform as they did here it will not be a season-spoiling issue. The Uruguayan's hat-trick was his second in two visits to Norwich and the catalyst for a dominant away performance. His second goal, just before half-time, was particularly special.

Michael Turner, handed the ball in uncomfortable circumstances on the edge of the area, was pickpocketed, nutmegged then given the best view in the house of Suárez's majestic finish with the outside of his boot.

"He's a special player, he's a wonderful player with great enthusiasm for the game," said Rodgers of the striker. "He doesn't get the rub of the green from officials, there's absolutely no question. Everyone today would have seen that. But we don't complain, we keep working and keep playing like that, and we'll be alright."

The starting XI was Liverpool's youngest in the best part of a decade. The presence of Suso, Andre Wisdom – both making first league starts – and Raheem Stirling meant the Reds kicked-off with three teenagers in their side, while last week 16-year-old Jerome Sinclair became the club's youngest ever player when introduced as a substitute in the Capital One Cup.

"A lot of people talk about the academies and players coming through but you still need to have a manager who has the bottle and puts his neck on the line by giving them a chance, and the manager has done that from day one," said the Liverpool captain Steven Gerrard. "He said to them from day one if they showed the right attitude and application in training he would give them a chance and they are doing well. We have a good mix of youth and experience and we as senior players will help guide them and show them the right way."

Second-half sloppiness led to two Norwich consolation goals – meaning that Liverpool have now gone nine Premier League games without a clean sheet – but the overall impression was one of utter dominance. Nuri Sahin, who scored the third, was hugely impressive at the tip of the midfield triangle, and Gerrard, who added the fifth, gave an intriguingly atypical understated display in the deeper role.

That could all give Rodgers a selection headache when Lucas Leiva returns to fitness in November. Norwich's concerns, on the other hand, run a little further than where their first win is going to come from. A trip to Stamford Bridge is next up before Arsenal visit Carrow Road.

"We knew this run of games would be tough and I'd have liked a few more points on the board," said the Norwich captain, Russell Martin. "We deserved a few more. That is why we are in the league. It should not be too hard to motivate the lads going to the European champions. We look forward to it." So, if the evidence of this Norwich display is anything to go by, will Chelsea.