Paul Benson's goal after 10 minutes saw them lead at Fratton Park for the first time since they beat Shrewsbury 3-1 on October 20.
But the visitors hit back with a Mat Sadler free-kick after 28 minutes and Billy Clarke scored the winning goal after 73 minutes.
With results and events off the pitch conspiring against administration-stricken Pompey, Whittingham said: "You've just got to keep telling the boys they're good players at this level.
"We've got to keep working on things, keep analysing things and show the boys where they're doing well on the video afterwards, so that they can see there are certain areas where they are doing well.
"But what we have got to do and what will lift confidence is if we defend properly. You think you've cracked it and then it comes and bites you back because we certainly didn't do that against Crawley.
"If we had defended the free-kick and the corner that led to their winner properly, we would have come away with a 1-0 victory."