Dockett, who signed with the 49ers this offseason, took to Twitter on Saturday to share his belief in his new team.
Davis, 25, cited his health Friday when he announced his retirement, joining 49ers teammates Patrick Willis, 30, Chris Borland, 24, and Justin Smith, 35, in walking away from the NFL this offseason.
Davis' retirement was the latest blow to a team already reeling from retirements, free-agency defections and cuts.
The Niners have now lost 12 players who started at least six games last season: Borland, Willis and Smith, plus running back Frank Gore (Indianapolis Colts), left guard Mike Iupati (Arizona Cardinals), linebacker Dan Skuta (Jacksonville Jaguars), cornerbacks Chris Culliver (Washington) and Perrish Cox (Tennessee Titans), receiver Michael Crabtree (Oakland Raiders), defensive lineman Ray McDonald (cut) and offensive lineman Jonathan Martin (waived/Carolina Panthers).
The team also traded punter Andy Lee, sending him to the Cleveland Browns on Saturday for a seventh-round pick in 2017.
New head coach Jim Tomsula will be charged with guiding the new-look 49ers, whose additions include former Baltimore Ravens wide receiver Torrey Smith, formerDetroit Lions running back Reggie Bush and Dockett, a defensive end who joined San Francisco after an 11-year run with the Cardinals.
ESPN.com 49ers reporter Paul Gutierrez contributed to this report.
49ers lose another veteran to retirement
ESPN 49ers reporter Paul Gutierrez discusses how San Francisco will be affected by the retirement of offensive lineman Anthony Davis, the fourth 49er to retire this offseason.