Sigurdsson has seen Iceland fail to qualify for next summer's Euros and also the resignation of coach Erik Hamren.
"It has been really difficult, and definitely some of the hardest days in our football careers. We have had some good moments in recent years, and maybe we have got used to it," Sigurdsson said.
"But we can not deny that this is really difficult. Maybe it was good that we had a new match right after, not because we have to forget it, but so we could continue and focus on a new tournament."
Sigurdsson is now traveling home to Everton and will not take part in Wednesday's match against England.
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