The work, part of the Local Transport Plan, was to resurface the road from the junction of Percy Terrace up to the entrance of the Duke's Middle School.
Instead, workers updated the road from the top of Hope House Lane (The Dunterns) down to South Street.
Coun Castle, who admitted his heart sank when he saw what had happened, said: "It must have been a misunderstanding.
"It is very unfortunate and I had to run the gauntlet of confused residents.
"I spoke to the engineer and as far as they were concerned they did the right job.
"But the work should have started at the junction of Percy Terrace and down to the entrance of The Duke's School."
He added: "That is what I asked for and requested in the Local Transport Plan, so how it has ended like this I don't know."
The work on Percy Terrace is now likely to be done next year when Lisburn Street and Prudhoe Street are resurfaced as part of the transport plan.
Other resurfacing measures included in the plan are Clayport Bank, Lower Barresdale and Greensfield Avenue.
Coun Archer joked: "We should give them a little picture map with "you are here" on so that they can find the correct street."