Poor defending from two Jamie McAllister free-kicks allowed Dominic Blizzard to open the scoring after 15 minutes and Byron Webster to double the Glovers' lead seven minutes before the break.
Pompey players went down the tunnel with boos ringing in their ears from their long-suffering fans but they bounced back with a spirited display in the second half and Paul Benson netted after 54 minutes to give the hosts hope.
They were unable to rescue a point, but Whittingham was pleased with his side's reaction after the interval and felt the fans responded fairly to a game of two halves.
"Our fans are probably the most loyal in the country that I've ever come across and they booed us off at half time - and they had every right to do that," said Whittingham.
"We told the players that you cannot come off a football pitch without giving everything you've got. The players had to be more positive and if they were, we knew the crowd would get behind them and applaud them off at the end - and they did.
"I think the fans were totally fair in the reactions they gave."
Whittingham hauled off ineffective striker Izale McLeod at half time, along with skipper Brian Howard who was nursing a groin problem. McLeod had already collected his fifth booking of the season for dissent and will miss the Blues' trip to Swindon on New Year's Day.
Whittingham was far from happy with his top scorer, who may have played his last game at Fratton Park as the transfer window approaches.
"It's not good enough," said Whittingham. "His last three bookings have been for dissent. He's going to miss Swindon now, where we're already struggling for players. He knew that as well. It's certainly not pleasing."