O’Neill gave Manchester United defender Jonny Evans, as well as unattached duo Corry Evans and Josh Magennis, the option of not travelling to games against Spain on June 8 and Andorra three days later, but the veteran trio all opted to join the group.
Winger Paddy Lane, on the other hand, told O’Neill that he felt he would “benefit from not being involved”.
Lane, who has four caps and started against Romania in March, scored 12 goals for Portsmouth, who won League One this season.
“We need to get away from that thinking,” remarked O’Neill, when asked whether it should be in team”.