The visitors led through a Stephen McManus own goal but conceded twice before the break to Henri Anier and John Sutton - resulting in a third straight defeat.
Johnston said: "Individual mistakes are costing us dear right now - apart from that with the second-half performance I couldn't ask for more. We need to defend better than that as a team and individually.
"We passed the ball really well in the second half and were unlucky not to get a goal. I think that performance typifies the way we have started the season."
Motherwell manager Stuart McCall said: "We've had times even last week when we had chances to kill people off.
"At 2-1 they are always still in it. There is more to come from us but we're delighted with three points.
"There is nothing like going into the international break on a win and we needed that."