The Welsh region have not won in Galway since 2004 and they made a slow start this time round as three Jack Carty penalties and a debut try for Nepia Fox-Matamua handed Connacht a 14-0 lead.
Tries for Sarel Pretorius and James Thomas brought the visitors within touching distance in the closing stages but Fionn Carr scored a breakaway try after great work from Bundee Aki to seal the win.
However, Tom Prydie's long-range penalty at the death secured a bonus point and Jackson says they must now build on the positives.
"We've got some great leaders in this squad and to be that far behind away to a tough team like Connacht and come away with something shows the character of the boys," Jackson told the South Wales Argus.
"We're gutted, because you never want to come out of close games on the wrong end of the score, but it will stand us in good stead.
"I'm told that the performance in first game in Connacht last year was a lot different to this one so if we can build on what we did against a strong side then we should have a good season.
"We've got a few new players in key positions that will take a little bit of time to gel but we are getting better and better every week as we get used to each other.
"Our attacking play can be very good and we showed glimpses of that against Connacht."
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