Coach Joachim Loew, who has just signed a 2-year contract extension, has provided a 27-man provisional squad which has left German fans in a state of confusion.
Remembering that he first walked through the doors of Italy's Coverciano training camp in 1978 with the under-14 team, Mancini said it was the right moment in his career to take on the challenge of coaching his country.
"We saw that it was not his season, not the normal form with his quality", Loew said.
Bayern striker Wagner misses out on the tournament as Loew favoured Stuttgart veteran striker Mario Gomez.
There are seven Bayern representatives in Low's squad, including Thomas Muller, Mats Hummels, Sebastian Rudy and Joshua Kimmich, but four players will have to be cut when the coach names his final 23.
Uncapped Freiburg striker Petersen received an invitation from the national team after scoring 15 goals in the Bundesliga this season.
Notable players on the plane to Russian Federation include Mesut Ozil, Jerome Boateng, Thomas Muller, Toni Kroos, Mats Hummels, Leroy Sane, injury-prone Marco Reus; and surprise inclusion of Bayer Leverkusen's highly-rated centre back, Jonathan Tah.
Germany faces Mexico, Sweden and South Korea in World Cup Group F. It plays its last warm-up games against Austria on June 6 and Saudi Arabia on June 8. "Some (of the reaction) seems to be over the top to me".