Tommy Wright was left frustrated as his St Johnstone team's 1-0 left them with one win in eight matches.
The tie at Ibrox was decided by Lewis Macleod's 86th-minute header.
"I thought we played particularly well on the night and to get nothing out of the game is disappointing," he said.
"Probably in the second half we didn't control the ball as much as we'd have like to. It was a decent performance but an unfortunate result."
St Johnstone had their chances, most notably when unmarked Frazer Wright headed Lee Croft's cross over the Rangers bar from eight yards in the first half.
After the interval, Steve Simonsen saved when left one on one with Saints striker Michael O'Halloran and the Rangers goalkeeper tipped a Brian Graham header wide but injured his shoulder in the process and had to be substituted.
"We had missed chances and they had missed chances as well," Wright told BBC Radio Scotland.
"Over the piece, we didn't make enough of the opportunities we had in the last third. I'd like to have seen people be a bit braver and take shots.
"I turned away thinking it [Wright's header over the bar] was in. I think Brian [Graham] was shouting at him to leave it because he was in an even better position. That was a good chance.
"We contributed to the game, but I do think in the second half we allowed them too many crosses into the box and too many free-kicks, which allowed them to put us under pressure, because they had great delivery from the wide areas.
"I thought it was a pretty entertaining game."
|St Johnstone manager Tommy Wright|
|"The players are saying it's all the little things we need to tidy up to get results. They produced one moment of quality to get a winner."|
Saints' Murray Davidson was taken to hospital as a precaution after he sustained a facial injury in a collision with Nicky Law, his midfield opponent.
Indeed, Davidson, who was stretchered off the pitch, tweeted: "On route to hospital to get checked out, needing stitched but hopefully the eye itself is ok! #gutted".
Despite his disappointment at the score, there were some bright spots for Wright.
"Gary McDonald came on and did extremely well," added the manager. "Hopefully, Muz will be all right for Friday night.
"Chris Millar did particularly well. He's got loads of energy and I'm glad to see him back fit for us.
"And I thought Michael O'Halloran - we played him through the middle - was excellent for us.
"I thought it was a good solid performance from us overall, but we just fell short.
"The players are saying it's all the little things we need to tidy up to get results. They produced one moment of quality to get a winner."