The Swans trailed at quarter-time against Gold Coast on Saturday, and led by just three goals at the main break before pouring in six goals to three in the final term for a 41-point victory at the SCG.
It followed last week's performance against Greater Western Sydney, when the young Giants got in front in the second quarter before succumbing by just five goals.
The Swans had a reduced pre-season due to their premiership win and were always likely to start slowly, but McVeigh believes his side needs to improve quickly, starting with next week's clash with North Melbourne in Hobart.
"I think we're just going at the moment," said McVeigh, who starred with 27 possessions, eight inside 50s, seven clearances and four goals.
"It'll be a step up again next week, but it was really pleasing that last 10 minutes (against the Suns) to see that pressure when the game was there to be won.
"I was really proud of that effort and we really have to continue it, because it goes up another level next week with North Melbourne."
His coach wasn't quite so damning, with John Longmire adamant the Swans had played well in patches early in the season, but he conceded they were yet to put together a complete game.
"I think we're just going in parts. That's the challenge," Longmire said.
"We've certainly shown in quarters that we are playing well. I think what we're doing is not putting it together for four quarters.
"When we are doing it we're doing it well and doing it strongly, and we saw that today in the last quarter.
"The challenge is to be a bit more consistent."
The Swans also had the distraction on Saturday of having their entire squad together on the ground 30 minutes before the opening bounce for the unfurling of their 2012 premiership flag.
The game then got off to a slow start, with both sides kicking first-term two goals in horrible conditions, before McVeigh led a much improved effort in the second quarter.
"It was a bit weird," McVeigh said of the pre-game ceremony. "We tried to just stay focused on the game.
"Obviously it's a great moment for the supporters and the support staff, but we were conscious of the game and starting well.
"It was a bit of a distraction, but a good one to have."
James Dampney is a reporter for AFL.com.au. Follow him on Twitter: @AFL_JD
