The striker made his confession after his second-half equaliser secured a 1-1 draw at Charlton Athletic.
Republic of Ireland international Idah struck midway through the second half to cancel out Charlie Kelman’s opener, earning Swansea a deserved point in south London.
Idah had been drafted in to start after an injury to leading scorer Zan Vipotnik.
But despite a dominant display after the break, Alan Sheehan’s side were left ruing a series of missed opportunities that prevented them from claiming all three points.
Swansea have won once in their last six matches in all competitions and are 16th in the table, five points adrift of the play-off places.
Although the result extended Charlton’s strong home record — they have now lost only once in their last 23 matches at The Valley — it also left Swansea frustrated to come away with just a point.
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That feeling was echoed by Idah, who admitted the players knew they need to start capitalising on their dominance.
"In some ways we are disappointed. The way we played the game was top and we probably deserved to get three points," said Idah.
"That's the fine margins and there were a lot of chances, including ones I had myself, which we have got to take.
"That's the difference for us this season, we have to take them when they come.
"The boys put in a shift and we dug in really well to get back in the game, so I think there are positives to take even though there is disappointment."
Idah’s performance was a bright spot, and his finish — a powerful, precise strike from 20 yards — underlined why Sheehan has shown faith in the 23-year-old forward.
"After the chance I had in the first half I was dying to get another opportunity," said Idah.
"Kaelan fed a really good pass into me, I could feel the defender was close to me, so I adjusted my body and took the shot on when I had the chance.
"I've got to be honest, I didn't actually know it had gone in at first. But it's really good for me to get on the scoresheet.
"Vipi had an injury and it meant I got a chance to show myself, to prove myself. So I am glad to have got the goal, but hopefully we can pick up three points the next chance we get for the supporters.
"They were brilliant, I said to the boys that it's a long way down here but they made so much noise throughout the game and when the equaliser went in it was like having a 12th man roaring us on.
“They were fantastic, fair play to them, we just wish we could have given them three points."
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Swans head coach Alan Sheehan shared his striker’s frustration, insisting his side had done enough to win the game but paid for a lack of cutting edge.
"I think we did more than enough to get the three points. We were comfortable in the first half," said Sheehan.
"We have a really poor start to the second half, misjudged a long ball and you are 1-0 down.
"But I think to come here, to deal with the direct play, the set-pieces, the transition - we did it really well for large parts.
"We took control of the whole second half. It was wave after wave and we should be coming away with maybe three goals again.
"We need to be more of a killer team if we are going to kill teams off because I am standing here very disappointed with a point."
For Charlton, manager Nathan Jones admitted his side were second best but was pleased to see his players grind out a result after a below-par display.
"We didn't play well. Did we not play well because we were bad or Swansea were good?" said Jones.
"Swansea are a good side, they have good players, they are well coached.
"At times we have to dust ourselves down. If you don't play well then don't lose. If you can't win a game then don't lose it, and that's what we have done today.
"I'm delighted for Charlie [Kelman]. He has been working tirelessly and getting little opportunities. It was nice to see him take one because that will be good for him."
The draw leaves Charlton eighth in the table, six points off the play-offs with a game in hand, while Swansea sit 16th — a position that belies the quality of their recent performances.
