"We had to put the ball in the net, and at critical moments in games we're conceding goals. It's very immature for us to concede at those moments," lamented Solomons.
"We play very well - we are improving all the time. We're playing good, constructive football, creating chances. We need to score but also close shop."
Swallows were classy in attack to score three quality goals from Lerato Chabangu (27th and 82nd minutes) and Vuyisile Wana (45th).
City made the score 2-1 in the first half with two goals in two minutes by Thapelo Tshilo (31st) and Puleng Tlolane (32nd). But they spurned chances to win the game in a half-hour period after the break where the Birds' defence were repeatedly split open .
"Swallows never threatened us often, and I think outside the times they scored they never had that many opportunities.
"We should have killed them. Sometimes it takes a bit of luck as well," observed the City coach.
It has been a tough start to the season for a team who survived relegation in their maiden campaign last season via the play-offs, with one win and three defeats.
Solomons, though, believes City can take comfort in their performances, and is hoping for a turning point against Orlando Pirates at Peter Mokaba Stadium on Saturday night similar to last season's 1-0 home shock of the Buccaneers.
By contrast, Swallows have had a bright start in results, but on the evidence of a shambolic defensive display, coach Zeca Marques has work to do maintaining it.
"I'm not Nostradamus but I wouldn't want to be in that [relegation] position again. So ja, it's a concern, but I think as the guys mature now and the new players get on board, we'll minimise that ," Marques said.