Ljungberg was appointed as caretaker boss at the Emirates Stadium after Unai Emery was sacked on Friday.
A seven-match winless streak in all competitions cost the Spaniard his job, but Ljungberg was denied victory in his first game in charge.
But Willock has hailed Ljungberg and insists the Gunners squad is fully behind the club’s former winger.
“To be honest, we know collectively that we need to improve, whoever the manager,” the midfielder told Sky Sports.
“Freddie is a brilliant manager. We believe in him and we are working hard to try and improve.
“He said the most important thing was to play with happiness, to get the pride in the badge back and to work to win.
“Every day in training we are trying to get that competitiveness back. I feel like [our luck] is going to turn in one game, and we can push on from there. It is coming, hopefully.”
Emery won only two of his final 11 Premier League matches in charge in north London.
The formerPSGand Sevilla head coach was criticised for his poor communication skills and his team’s absence of an on-field identity, but Willock still praised the departing 48-year-old.
“Friday is in the past now. Emery was a very good man, a very good manager,” he added.
Ljungberg’s side then conclude the Europa League group stage against Standard Liege, against whom they must avoid defeat to guarantee a place in the knockout stage.