Liverpool's horrendous season went from bad to worse on Sunday as Wayne Rooney, Juan Mata and Robin van Persie ran riot at Old Trafford.
The defeat increased the pressure on manager Brendan Rodgers, with last season's runners-up languishing in 11th position after claiming just two wins in their past eight league matches.
Dudek, who played a leading role as Liverpool won the 2004-05 UEFA Champions League final, stressed that Rodgers and his players must unite to get their season back on track.
"I think everyone is under pressure at the club," Dudek said after Liverpool were drawn against Besiktas in the Europa League round of 32. "They had a good season last year, and because of this there is high expectation this season.
"I think they missed [Luis] Suarez, and because of that they're all under pressure. The boss, the players, but they need to stick together, working hard, especially now before Christmas, and try to sort things out very quickly.
"Liverpool, when they fight altogether they get results. When they have lack of fighters on the pitch they are struggling to get results, they need everyone on board and fight to the end."
Liverpool were busy during the off-season, recruiting no less than eight players.
Adam Lallana, Dejan Lovren, Lazar Markovic, Alberto Moreno, Mario Balotelli, Emre Can, Rickie Lambert and Divock Origi (loaned back to Lille) were all signed as Rodgers attempted to challenge for honours in both the Premier League and the Champions League.
But the new arrivals have failed to make an impact and Dudek fears they be may fighting for their Liverpool careers.
"With the new signings, you never know what's going to happen," said the Pole.
"You think they're good because they had a very good spell at their previous club, and you hope they'll play as well for Liverpool. But they needed time, sometimes they love to play, some will never play.
"Liverpool is a special club with a special coach as well, with very high expectations and some of the players need more time, but I don't know if they will have that time because Liverpool needs results straight away."
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