The Citizens drew 1-1 with League Two rivals Albion Rovers on Saturday in their third Premier Sports Cup Group E fixture before losing the penalty shootout 5-4 at Cliftonhill.
Declan Byrne netted after just four minutes in Coatbridge before James Hilton restored parity with 20 minutes left to take it to a shootout – City's Ouzy See, Lewis Kidd and Scott Reekie all seeing their spot-kicks saved.
Naysmith's side cannot progress to the knock-out stages of the competition following previous defeats to Championship sides Hamilton and Ayr United.
"You have to take pride in your defending – like we saw the Italians do in Euro 2020 – we have to get that into our game and stop conceding early goals," Naysmith explained. "We were slow to organise the wall and I was disappointed that, when the free kick came off the bar, Albion Rovers were first to react.
"In certain parts of the two previous games we played well but Saturday was about putting in a more complete performance, and I think that, even though we lost on penalties, for the majority of the game we were the better team.
“We certainly had two or three chances to get ourselves level in the first half that we never took. But when they get them we were relying on Ryan [Goodfellow] to make a couple of good saves. For t he last 20-25 minutes I thought we were the team on top. Our fitness was good. That’s three games in a week and we looked to be the team finishing the game stronger.
"There are definitely areas to improve on, but there were good things as well that were pleasing. I'm unhappy about us not being organised at a set-play three minutes in. The small details can come back to hurt you and that's what happened."
Summer signing Michael McFarlane, a youngster recruited from St Johnstone, was handed his first start in senior football after impressing as a sub in previous games.
Naysmith added: “He’s someone we can develop. He deserved his start and can only get better the more we work with him.”