Rory Loy put the visitors ahead after 51 minutes before a Liam Walker penalty rescued Pompey a point with 12 minutes left.
The Blues have now gone 21 games without a victory but Whittingham believes Pompey's first win since October 20 is within reach, despite watching his side sink to the bottom of the League One table.
He said: "Confidence is the biggest thing for any footballer. If they're confident in their ability and confident when they go out there with their team-mates week in and week out, they'll play better. It's improving.
"I think the players feel themselves that things are changing slightly. It's not going to be a quick turnaround when you're coming off the back of the run we've had and you're in the run we're in. it's probably one we might have lost a few weeks ago and heads might have gone down after we went a goal down. So that shows there is a spirit building there."
Whittingham started with Patrick Agyemang up front and brought John Akinde off the substitutes' bench. The duo formed a powerful strike partnership and gave Pompey the muscle they have lacked in the final third.
"That's the reason for bringing them in," Whittingham said. "They are in a position where they haven't played many games and we have to be careful how much we throw them in. We want them for the whole season. We don't want to lose them to injury so we're being careful how we introduce them."
Carlisle boss Greg Abbott admits his side blew chances to secure victory and believes a gritty performance from financially-troubled Pompey earned them a draw.
He said: "Portsmouth are playing in emotion country at the moment and that's probably what got them the point. They'll think they deserved it and we're aggrieved we didn't get three. But I'm not complaining too much.
"Rory is kicking himself he didn't get a couple more goals or maybe even a hat-trick. That's the difference between winning and losing games. We feel aggrieved we haven't got the three points, but that's football. You have to get that second goal - it cements victories. We didn't get it."