Jackson's first chance came in the 52nd minute but he could only sting the hands of Adam Collin. The striker had another great opportunity deep into injury-time but screwed his shot wide from six yards following good work from Andy Barcham.
It was Barcham who had the best chance of a dull first half after 20 minutes, breaking through the Carlisle midfield only to fire too close to Collin.
Carlisle's best opportunity before the interval fell to Vincent Pericard, but the former Stoke frontman headed wide from 12 yards.
Gillingham were dominant after the break but couldn't find a way through and Ian Harte almost snatched victory for Carlisle with a late free-kick.