Both players had been tipped to feature in Stephen Kenny's first senior Republic of Ireland squad but they missed out on this occasion.
Obafemi made his feelings known with a tweet after the squad was announced.
The Southampton striker, who scored three goals in 25 Premier League appearances this season, appeared unhappy with the decision.
The pair are joined in Crawford's selection by a number of others who were linked with the senior squad, including Jason Knight and Will Smallbone.
The 25-man squad will report for a four-day training camp in Northern Ireland from Monday, August 31st to Thursday, September 3rd.
Ireland Under-21s have three crucial qualifiers in October and November against Italy, Iceland and Luxembourg and the training camp will provide crucial preparation time.
St. Patrick's Athletic defender Luke McNally receives his first Under-21 call-up as well as Southampton duo Will Ferry and Will Smallbone. Watford striker Ryan Cassidy will also report for the Under-21s for the first time.
Shamrock Rovers and Bohemians' Dublin derby clash on September 5th has been postponed due to the involvement of Liam Scales and Neil Farrugia (Rovers) along with Danny Mandroiu and Danny Grant (Bohemians).
: Caoimhin Kelleher (Liverpool), Gavin Bazunu (Rochdale, on loan from Manchester City), Ed McGinty (Sligo Rovers).
: Lee O'Connor (Tranmere Rovers, on loan from Celtic), Danny McNamara (St. Johnstone, on loan from Millwall), Darragh Leahy (Dundalk), Conor Masterson (QPR), Liam Scales (Shamrock Rovers), Luke McNally (St. Patrick's Athletic), Nathan Collins (Stoke City), Dara O'Shea (West Bromwich Albion), Thomas O'Connor (Southampton).
: Dan Mandroiu (Bohemians), Jason Knight (Derby County), Jack Taylor (Peterborough United), Will Ferry (Southampton), Will Smallbone (Southampton), Conor Coventry (West Ham United), Connor Ronan (Grasshoppers Zurich, on loan from Wolverhampton Wanderers).
: Michael Obafemi (Southampton), Danny Grant (Bohemians), Jonathan Afolabi (Celtic), Zach Elbouzedi (Lincoln City), Neil Farrugia (Shamrock Rovers), Ryan Cassidy (Watford).