"We played as well as them. But they had three chances and scored each one.
"When the third one went in I feared it was over.
When you are 3-0 down in the Champions League, it is difficult to think about going through.
"We can score goals and we now have to believe in ourselves."
But Vieira accepted that Arsenal must improve.
"Last year we believed in ourselves and we have to do that again."
Defender Alex headed in an early goal to give PSV Eindhoven a 1-0 home win against Monaco in their Champions League last-16 first leg. The Brazilian defender rose unmarked near the middle of the box in the eighth minute to direct Mark van Bommel's corner in off keeper Flavio Roma.