Jackson grabbed an unlikely leveller after his shot deflected off Town defender Christophe Berra and past the wrong-footed Dean Gerken.
At the other end, Addicks goalkeeper Ben Alnwick was also a hero after saving David McGoldrick's 78th-minute penalty after Ipswich had taken the lead through a Richard Wood own goal.
Powell believed his side deserved a point from their trip to Portman Road - a belief backed up by his counterpart McCarthy.
Powell said: "We could have been walking away with a defeat when I think the minimum we deserved was a point. The performance, especially in the second half, warranted it.
"Johnnie got the goal but Ben made a good save from the penalty. He has been first-class since we brought him in."
While their objectives remain at different ends of the Sky Bet Championship, both sides enjoyed an unbeaten Christmas and New Year programme.
Powell said: "The players have been excellent over the festive period. They are a bit more confident and are showing a bit more passion and that comes with results.
"The position we are in means every point is priceless."
Ipswich were guilty of sitting back as the game wore on, while both sides had decent shouts for penalties turned down before the home side was eventually given one.
Prior to McGoldrick's miss, Ipswich had led since the 23rd minute when the excellent Daryl Murphy broke clear down the left and his teasing low centre was turned into his own goal by the unfortunate Wood.
And the in-form home side, who have now gone eight matches without defeat, almost guaranteed the three points after being awarded a second-half penalty.
Charlton midfielder Jordan Cousins needlessly barged into Paul Anderson in the area but top scorer McGoldrick's spot-kick was saved by a combination of Alnwick and the post.
It was a miss that would prove costly after Jackson's dramatic late leveller.
Ipswich manager McCarthy had little complaints in his summing up of the match.
He said: "It was a tough old game in terrible conditions, but a fair result. The conditions had a big part to play and it took a deflection to beat us.
"But overall they deserved a point. We could have killed it off with the penalty but Didds (McGoldrick) has been brilliant so I can have no recriminations about that."
Unbeaten in eight matches, Ipswich remain in the Championship play-offs and McCarthy added: "We are in the top six on January 1. We could have had two more points today but we are in a good position which is testimony to the lads, who have been brilliant."