Barca fell to a third consecutive defeat to bitter rival Madrid in all competitions for the first time since 1978 as it missed out on the chance to move top of LaLiga.
Oscar Mingueza set up a thrilling final half-hour at Estadio Alfredo Di Stefano when prodding in to halve the deficit after first-half strikes from Karim Benzema and Toni Kroos.
The visitors attempted 12 shots in total in the second half, three of those on target, and nearly snatched a point when Ilaix Moriba struck the crossbar in the 94th minute.
However, Koeman felt his side should have had a penalty when fellow substitute Martin Braithwaite went down in the box under pressure from Ferland Mendy.
😡 @RonaldKoeman labelled this incident a "clear penalty" 👀 Do you agree? The officials didn't, leaving the @FCBarcelona boss LIVID after another #ElClasico defeat to @realmadrid. More here 👉🏻 https://t.co/gP3QfSTbzG #LaLiga | #RealMadridBarcelona pic.twitter.com/cQp4Pe150j— beIN SPORTS (@beINSPORTS_AUS) April 10, 2021
The Dutchman also questioned why more time was not added on at the end as a portion of the four allotted minutes was taken up by the officials resolving a technical issue.
"If you're a Barca fan or a Barca player, you're very unhappy with the result because I think there were two clear decisions that the referee didn't make that would have changed the game," he said.
"I think we weren't good at all in the first 45. We weren't good in attack and we weren't good in defence.
"In the second half we improved but I only ask for a bit better when making key decisions because they are decisions that could have cost us the game and eventually they did.
"I think the added time as well was four minutes and it should have been added on.
"He only added two minutes because of the issue with his microphone and there were quite a few more stoppages, also with the possible penalty towards the end. Once again, we have to accept it and shut up."
Defeat for Barca was its first in 20 league games since early December and saw it drop to third in LaLiga, a point behind Real Madrid and Atletico Madrid, the latter playing its game in hand against Real Betis on Monday (AEST).
When asked if the two decisions that went against his side were defining moments, Koeman said: "Yes, of course.
"The issue with the referee's microphone is a different issue completely. Obviously there were many things on the pitch that affected the result overall.
"But I do think we should have gotten a clear penalty towards the end and I don't know why it wasn't reviewed by VAR [video assistant referee].
"The linesman is there, he should assist with the decision. Everyone probably thinks it's a penalty. Do you think it's a penalty?"
The Barca boss to cut short his post-match interview after the reporter failed to answer his question, clearly showing his frustration at a result that could cost his side a title many were expecting it to win.
Koeman is the first Barcelona coach to lose his first two LaLiga games against Madrid since Joaquim Rife in 1980, who also lost his first two Clasicos to Los Blancos.