The 36-year-old striker, who retired from international football after the Euro 2012 Championship finals, was offered the position last week.
But he believes he is not qualified to take over as boss of the Ukraine national side.
He said: "I consider that taking over the national squad will be a bit too hasty a move for me.
"I hope that the FFU will accept my decision with understanding.
"I'm really grateful to the FFU and our football chief (Anatoly) Konkov for their top-level trust in me which they showed by offering me the post of the national manager."
Last week Ukraine football supremo Konkov offered Shevchenko the post, which remains vacant since Oleg Blokhin's departure for Dynamo Kiev in September.
Konkov said: "Shevchenko has experience of playing in great clubs such as Dynamo Kiev, AC Milan and Chelsea under the management of legendary coaches Valery Lobanovsky, Carlo Ancelotti and Jose Mourinho.
"He had a unique opportunity to adopt their methods, their knowledge and talents.
"Just remember that unknown young coach Josep Guardiola (Barcelona) has achieved tremendous results in just several years.
"I'm confident Shevchenko is also capable of achieving serious heights as the national team's manager.
"He has enough experience and character for it. The federation, meanwhile, will provide him with all the necessary help in his work."