The Reds languish in ninth spot on the ladder ahead of hosting Western Sydney Wanderers on Saturday night.
Veart's troops have just one win from their past eight games, with four losses and three draws in their slump.
The Reds are six points adrift of the Wanderers, who currently hold the last of the six finals spots, but Veart says the playoffs remain on his agenda.
"We have still got nine games to go," he told reporters on Friday.
"We believe that we can make the finals this year.
"We know history says you need to get around the 35 point mark so that's six (more) wins.
"We're more than capable of doing that. We will keep fighting right to the last game of the season."
Adelaide will be without frontman Hiroshi Ibusuki for at least a week due to a hamstring strain, while Josh Cavello will be sidelined for the longer term due to a thigh injury.
The Reds have summoned young gun Nestory Irankunda, Nick Ansell and veteran Ben Halloran, who was axed last-start.
Veart said Halloran had responded to his omission in proper fashion.
"Just the energy, that's all we're looking for, to work hard," he said of the 31-year-old.
"It's not just working hard on match day, you have to work hard during the whole week as well.
"And sometimes you need a little bit of a reset and he has trained really well this week."
The Wanderers travel to Adelaide with a superb recent record over the Reds - they've lost just one of their past seven clashes.
And Western Sydney haven't been defeated in Adelaide since November 2017, a stretch featuring three wins and four draws.
In contrast, Adelaide's usual fortress at Coopers Stadium has been repeatedly breached this season, with the Reds winless from their past four home games.
"They're all tough (opponents) at the moment," Veart said.
"Wanderers are physically a very strong side and make it very difficult for you.
"There's no easy games in the A-League and you have got to work hard for your wins."
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