The Stoke City man admits to being bemused over two of Liverpool's best players refusing to put their names forward for penalty duties.
Manchester City edged the shootout 3-1 at Wembley, with goalkeeper Willy Cabellero the hero after saving from Lucas Leiva, Philippe Coutinho and Adam Lallana, after Emre Can scored the Reds' first spot kick.
Captain Henderson and striker Sturridge were conspicuous by their absence in the pecking order, with the club's fans - including the legendary Jamie Carragher - criticising them on Twitter afterwards.
The decision not to include themselves has also incurred the wrath of former Reds midfielder Adam, who cannot understand why the pair shirked the responsibility.
"If I'm captain of the club I'm first up, if I'm supposedly England's best striker I'm second up," Adam, now at Stoke City, said on BBC Radio 5 live.
"Jordan Henderson is a shy character, so maybe he doesn't feel like he had to step up. But you've got to have the bottle to be able to stand up."
The match had finished 1-1 after 120 minutes of play, with Philippe Coutinho's 83rd-minute equaliser cancelling out Fernandinho's opener early in the second half.
Sturridge, whose season has been hampered by injury, hardly excelled in regulation, and his failure to step up for a penalty only added to the fans' frustration with him on the day.
Henderson took over the armband from Steven Gerrard at the beginning of the season.