Suarez had two goals before half-time and went on to provide the assist for Nuri Sahin to find the net before adding his third.
Liverpool had failed to record a victory in the Premier League prior to Saturday's contest but have now won three of their last four games in all competitions.
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"It's a privilege to be able to play alongside Luis," Allen told the Liverpool Echo. "I'm just grateful he's on my team. When you're out there playing alongside him, you just have to be in awe of a performance like that.
"The goals, some of the things he did, not many people in world football can do. He's got everything you need to be a top-class striker and I'm excited about the season he's going to have for this team.
"We mentioned before the game about the fact he got a hat-trick against them last season. The fans at Carrow Road must be happy to see the back of him."
Allen sat at the base of a midfield three that also included Sahin and Steven Gerrard, who both grabbed goals in the second half as Liverpool cruised to three points.
The Wales international insists that the Reds had been unfortunate not to win earlier in the campaign and claims that few teams will be able to match Brendan Rodgers' side at the top of their game.
"The three of us really enjoyed playing together," Allen enthused. "We've all got that similar sort of style in terms of passing. The passing and movement was good and that meant we were able to control large parts of the game.
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"It was a great way to get that first league win and we felt that it's been coming for a while. Despite a few disappointing results, we haven't been playing badly.
"We haven't had that bit of luck at times when we've needed it but we've just kept working and concentrated solely on ourselves.
"This is where our seasons starts really. We have to kick on from here. If we keep performing like that then it will be the first win of many.
"With the talent we've got in the team we know that if we give it everything then there's not many teams who can stop us."