Pompey were leading 2-1 with just 10 minutes remaining, courtesy of goals from David Connolly and Shaun Cooper after Bradley Wright-Phillips' opener for the Bees.
But Wright-Phillips equalised in the 85th minute and then his slide-rule through ball 60 seconds later was converted by Clayton Donaldson to seal a 3-2 win at Griffin Park.
Whittingham said: "I'm not pleased because you're never pleased when you lose, but I can't fault the spirit of all of my players.
"We controlled Brentford for much of the game and got stronger as the game went on, especially after we scored the second.
"But you have to do it for 90 minutes or it means little."
Whittingham added: "After all we have been through in recent months and this week the spirit of the side was incredible so there are plenty of positives for us to work on.
"Brentford play the ugly game very well but they can play football as well, so for us to match them as we did was superb and is a very good sign for the future.
"I'm just disappointed that we couldn't see it out for our magnificent fans."