Meanwhile, the Dogs have been left to contemplate being beaten by a team that "defended a lot better than we did", according to coach Brendan McCartney.
Fremantle, which got through the game no "dramatic" injuries – a calf corkie to Clancee Pearce and a knock sustained by Michael Johnson the only ones reported – was pleased to have started well after struggling to do that in round one against West Coast.
But Lyon said there were still "inconsistencies" to work on.
"I think once you're satisfied, you're in trouble, aren't you?" Lyon said.
"We came here to get the four points, good teams win interstate and if you want to be a good team you have to win interstate and we've done that.
"We're doing that on a consistent basis."
Lyon also said the game was a run his side needed to have after playing their round one game two weeks ago although was adamant having a week off so early in the season wasn't a hindrance.
"We've played two games in five weeks, basically. I think that's roughly right," he said.
"You just play with what's put in front of you but it gave us some real freshness and bite early.
"The boys were exceptional on the training track so it gave us some confidence that we would play well but there's just that mental and physical fatigue, that match hardened, early round … we just fell away.
"At times we were really pleased and other times … we need to get it done a bit more consistently."
Lyon said he wasn't aware of Matthew Pavlich carrying any injury other than the mending split hand webbing he sustained against West Coast, despite the captain having treatment on his calf at quarter-time.
Pavlich kicked two goals, three behinds and had a hand in three other scoring attempts but didn't appear himself at times.
Meanwhile, McCartney said while his players were "too easy to play against" at times, there were other areas of the performance that were pleasing.
He said it was "another good step in the right direction against a professional, mature, disciplined footy team" despite the Dogs' kicking efficiency dropping off from last week's win over the Brisbane Lions.
"[Fremantle] values the part of the game when you haven't got the ball, and it's a part of the game that stacks up well when it really matters because you can't always have the game on your terms at AFL level," McCartney said.
"We believe they're as good as it gets in that side of the game. When I say they defended better, it wasn't like we were a basket base at it but they were more consistent over the period of the day."
There were still other positives for the Dogs, including the fact many senior players – including Robert Murphy, Daniel Giansiracusa and Shaun Higgins – were down and they still managed to get the ball forward and win the clearances.
One was young midfielder Tom Liberatore, who had 28 disposals, a staggering 12 clearances and shone when it came to the inside work.
"He's going to become elite at it, there's no doubt, provided he keeps working hard and respecting the game and respecting his role in the team," McCartney said.
"He's got other things to add to his game but he's certainly going to become a very special player in that inside part of the game."
Adam Cooney was another highlight, with his movement the cleanest it's been in two seasons across his 90 per cent of game time.
"I had a good pre-season and was running on top of the ground. I did 80-90 per cent of the pre-season coming in so that gave me a huge amount of confidence," Cooney said.
Former Fremantle player Nick Lower curbed the influence of David Mundy in the first half and kept the ball winner to 17 disposals, which pleased fellow tagger Liam Picken.
"I suppose I can play a range of positions [with Lowerin the team]. I was playing in the backline today," Picken told AFL.com.au.
"It's great; he's been really good in the midfield, helping out, and he's had a really big impact since he's come, which has been really good."
Captain Matthew Boyd will be considered for Sunday's clash with Richmond at Etihad Stadium but not "if there's any element of doubt" on his fitness.
Matthew Pavlich is a forward in NAB AFL Fantasy. He averaged 95 points in 2012. Register your team at our AFL Fantasy Hub.
Jennifer Phelan is a reporter for AFL Media. Follow her on Twitter @AFL_JenPhelan.
