That four-try reverse saw them miss out on a golden chance to close the gap on the sixth-placed Scarlets in the race to finish as the nation's second-best region, with a slow start seeing them trail 14-3 just past the first quarter at Rodney Parade. They never recovered from that frustrating opening as they fell to a third home defeat to Irish opposition this season after a fine win over Ulster was followed by narrow losses to Leinster and Munster.
Jones admitted that his side were well below par on Sunday afternoon, with the former Ospreys and London Welsh boss claiming that it felt as though they were 'back to square one' after all the bad habits associated with Gwent rugby came back'.
"The whole squad is embarrassed by some of the skill levels and decision making against Connacht. As coaches we need to step up and the players need to step up," said Jones.
"We've had issues in our tight play all season but the rest of our game has been far better than other teams. That collapsed against Connacht and left us with our pants down. It's up to the players to pick themselves up, go out to Zebre and pull something out of the bag."
Jones will certainly hope to see a positive response to those comments at the Stadio XXV Aprile, a venue where the Dragons edged to a 14-13 victory in February of last year. Both home games against the league's newest side in Newport have ended in comfortable 30-7 and 37-6 successes but there is no danger of complacency from the Dragons given the closeness of their last visit and Zebre's win over Cardiff Blues at the same venue in February.
The Dragons fly to Parma having only won once away from home in the PRO12 since their last trip there 13 months ago, with a fine victory at Glasgow in November sandwiched by 10 disappointments on their travels.
As for the Italians, they go into the game on the back of a 27-0 drubbing at leaders Leinster last weekend but their previous fixture was that famous win over the Blues, when they backed up September's shock victory in Cardiff with a 15-10 win on March 1.
A victory of any sorts for the Dragons would see them move to within a single win of the Scarlets, over whom they currently have a game in hand, with Simon Easterby's side facing Connacht on Sunday.
The back three remain the same, but it is all change in the midfield as Pay Leach and Ashley Smith come in to replace Ross Wardle and Jack Dixon, who drops to the bench.Jones has named a new front row of Phil Price, Wales U20 hooker Elliot Dee and Duncan Bell.
Skipper Andrew Coombs is joined in the second row by Matthew Screech, who takes over from Rob Sidoli, while the back row sees Wales No 8 Taulupe Faletau return to the starting XV.
There are also seven changes to the replacements as Sam Parry, Bruce Douglas, Nathan Buck, Cory Hill, Jevon Groves, Jack Dixon and Hallam Amos all join Wayne Evans.
Dragons: Dan Evans; Tom Prydie, Pat Leach, Ashley Smith, Will Harries; Jason Tovey, Richie Rees; Phil Price, Elliot Dee, Duncan Bell, Andrew Coombs (c), Matthew Screech, Lewis Evans, Nic Cudd, Taulupe Faletau.
Replacements: Sam Parry, Bruce Douglas, Nathan Buck, Cory Hill, Jevon Groves, Wayne Evans, Jack Dixon, Hallam Amos.