The announcement to part ways with the trio comes one day after the Falcons posted a 34-32 win over the Tampa Bay Buccaneers to wrap up a 7-9 season.
Head coach Dan Quinn will serve as the team's defensive coordinator, the team announced.
"We know we have a group of players here we are excited about and in order for us to consistently play true to our identity in all three phases we thought we needed some changes," Quinn said in a statement.
The 44-year-old Sarkisian, however, was unable to return the offense to its Super Bowl-caliber level it had under Shanahan despite featuring former NFL Most Valuable Player Matt Ryan and six-time Pro Bowl wideout Julio Jones.
"Sark has shown he's a good coach and play caller," Quinn said. "After evaluating the entire season, I decided it was necessary that we had a new voice and direction for our offensive unit."
Manuel, who spent four seasons with the Falcons, initially served as the secondary coach/senior defensive assistant before spending the past two years as the team's defensive coordinator.
The Falcons finished in the top 10 in both scoring defense and total defense in 2017 before seeing those totals dip significantly this season. Injury-riddled Atlanta allowed an NFL 25th-best 26.4 points per game in 2018 and 384.5 yards per contest, which ranked 28th.
"Marquand is a talented coach and excellent teacher that I have coached with for a number of years," Quinn said. "I believe he should have the opportunity to call plays for a defense, so we have decided to allow his contract to expire so he can explore those opportunities."
Armstrong spent 14 seasons with the Falcons, serving as safeties coach from 1994-95 before being promoted to secondary coach in 1996. He rejoined the organization in 2008 as Atlanta's special teams coach, which he held for 11 seasons.
"Coach Armstrong helped develop some really good players on our kicking units over his time here," Quinn said. "Special teams has to be the gateway to the identity of our football team. In order to see that, we felt we needed a new voice and design. We wish Keith nothing but the best in the future."