Former South Africa and Italy boss Mallett was Lancaster's main rival throughout the selection process.
"I would like to congratulate Stuart Lancaster on his appointment as England Rugby head coach," Mallett said in a statement.
"I am sure he will continue to build on the good work he has done with the team in the aftermath of a difficult World Cup for them.
"I believe the process was conducted in the most professional manner. I gave it my best shot and was glad to be able to discuss my feelings and philosophy on how I'd have coached the team."
Lancaster guided England to second place in this year's Six Nations as interim coach.