A week after bringing former captain Stefan Mauk back to Adelaide, the Reds have persuaded Dukuly to return from Stade de Reims in France.
United, winners just twice in their past 10 matches, have drifted to eighth on the ladder ahead of Friday night's home game against 11th-placed Perth Glory.
Asked if it was the worst period since he was appointed coach in September 2020, Veart said: "Definitely since I have been in charge.
"We're normally winning a lot more games, at home especially," he told reporters on Thursday.
"You need to sometimes win an ugly game to give you that little bit of a boost to push on and get that belief back.
"But in saying that ... we just have to work harder.
"The games that we have lost haven't been through the other team out-playing us. It has been more from our own effort.
"We have had a few good tough discussions with the group over the last couple of weeks."
Dukuly returns in the wake of Adelaide's horror 4-0 home loss to Central Coast last week.
The 21-year-old played 14 games for the Reds before moving in July 2022 to France, where he made 30 appearances for Stade de Reims' reserves without cracking a first-team berth.
Veart hailed the return of the speedster as important with his side three points ahead of the struggling Glory but also just three shy of Melbourne City in sixth spot.
"He is a quality young player," Veart said.
"He has been away in that different environment for the last nearly 18 months so he has developed his game a fair bit ... he's developed his mental toughness as well.
"He will come back and definitely provide an attacking threat."
Veart said he would have liked more signings during the transfer window.
"We just couldn't find the players that we were looking for," he said.
"So we have to push on for the rest of the season.
"The squad is, when we play at our best, we're good enough.
"We just have to fix those inconsistencies that we've been having, especially over the last couple of months."
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