The Arsenal manager, Arsene Wenger, has yet to sign a direct replacement for the midfield player having missed out on the Brazilian Julio Baptista, who opted for Real Madrid ahead of Highbury.
But even if Wenger decides not to splash out, Bergkamp is confident Arsenal can win the title by relying on youngsters like Cesc Fabregas and Mathieu Flamini. "Patrick was a big, big player for us on and off the pitch. He helped to build what we have now, we shouldn't forget that," Bergkamp said.
"How will we cope? Well, we have won games without him in the past and we will stick together and come out of it hopefully stronger, because we have to. If you cannot be competitive with the money then you have to look at different things - the young players, the youth system.
"We are still a team with a lot of talent and if we can keep it together and let it grow then we can still be a good team. This season there is still a possibility we can be champions. We have not given the title to them already."
Arsenal have already signed Alexander Hleb, the versatile Belarus midfielder, for £10m from Stuttgart, but he is not a like-for-like replacement for Vieira.
Newcastle's Jermaine Jenas has been linked with a move to Highbury and when it appeared Vieira was off to Real Madrid last summer, Michael Carrick was targeted by Wenger. But neither player offers Vieira's central presence on the field or leadership skills.
Wenger has turned to Thierry Henry, a quieter, almost introspective figure on the field, to captain Arsenal this season and Bergkamp believes he will grow into the role.
The Dutchman said: "I am sure that if you had a choice you would take a defensive midfielder or a defender as captain. It is totally new for Thierry. Like a lot of strikers he is busy with his own game because we have to make a difference. But he wants the job. He certainly has the character to combine the two."
Wenger has an eye out for a new goalkeeper after neither Jens Lehmann nor Manuel Almunia proved overly reliable. Uruguayan Sebastian Viera is on the list but a deal remains some way off, said Wenger.
Wenger will decide tomorrow whether to sign triallists Alexander Song, a 17-year-old midfielder, and former Barcelona defender Philippe Christanval.Reuse content