The West Yorkshire club surged from bottom in May to finishing the regular campaign in fifth with nine wins from their last 10 games under new head coach Simon Woolford.
However, they are still six points adrift of fourth-placed Warrington Wolves ahead of Friday’s Super 8s opener at leaders St Helens and accept they will, realistically, need to win all seven games to stand a chance of making the top-four semi-finals.
McGillvary told The Yorkshire Post: “It is out of our hands but the pressure is actually back on us. Last season we just reached the Super 8s and there was no concerns as we were safe.
“But we know how that ended. We only won twice more before the end of the season and people are saying similar things now about how we are in there and so not in any danger of relegation.
“But we want to put pressure back on ourselves. We’ve given ourselves a chance of doing something special and don’t just want to make up the numbers.
“We want to keep pushing on and stay in contention while building on what we’ve started for next season.”
Huddersfield’s task will not be easy, though, especially as they head to a Saints side expected to make an immediate response after Sunday’s shock Ladbrokes Challenge Cup semi-final defeat to Catalans Dragons.
It was just the third loss of the entire year for Justin Holbrook’s team who thrashed Giants 66-4 in their last meeting in April.
But McGillvary, 30, believes the visitors can take heed of what dogged Catalans did, bullying Saints up front with former England hooker Micky McIllorum gaining particular praise.
“I didn’t see the game live but saw some clips this morning as part of our video session and Catalans were absolutely outstanding,” he said.
“Their pack performance was one of the best I’ve seen for a very, very long time. Micky McIlorum led it brilliantly; his line speed and courage in defence, getting in front and shutting them down in the middle, was superb.
“I’m glad for him and you can see why he’s a Challenge Cup, Grand Final winner and an England international; he always comes up with the performance when it really matters and puts his body on the line.
“For us to even come close to beating Saints, we need to have a bit of that steel, too. It was amazing. I know we can do that; we’ve won nine out of our last 10 games and that’s not by accident.
“Our forwards have been outstanding and they have been setting the platform for us backs. We’re definitely capable.”
Certainly, there is real confidence running through Huddersfield at this moment, something McGillvary puts down to the impact Australian Woolford has had since arriving as Rick Stone’s successor in May.
The appointment of his fellow countryman Mark ‘Bumper’ Andrews as performance manager, too, has yielded rich dividends.
“There’s been a lot of tweaks especially to our defence, which is a whole lot better now,” said McGillvary.
“At the start of the season, we were shipping a crazy amount of points; if we gave away a penalty it often turned straight into us giving away a try.
“But Simon and ‘Bumper’ have brought a new fitness regime that has really helped us get fit enough to defend properly.
“There are certain specific things you can do to gain that sort of fitness for rugby league and Mark Andrews is qualified to do that so bringing him in has been great. It’s helped us to do what we’ve been doing in games, learning to really handle oppositions.
“It then goes hand in hand; the better you defend, the more energy you have to attack.”
McGillvary has taken his tally for the season to 10 tries with back-to-back hat-tricks in wins against Castleford Tigers and Wakefield Trinity.
“Everyone thinks I’m suddenly playing well but before those hat-tricks I thought I was going decent,” he insisted.
“It’s always nice to score but the team’s the main thing and I’m just getting on the end of what they’re doing. Leroy (Cudjoe) has set most of them up for me.”