Earlier this year, the teams agreed to allow blanket-free full wets from the Emilia Romagna GP onwards.
After the Imola event was cancelled, the tyres were used for the first time by three drivers in the Monaco race and were then tried by the whole field in FP3 in Canada.
As Pirelli works towards the possible introduction of blanket-free slicks for 2024, the company wanted to fast-track its new intermediates into race weekend use within this season.
The Singapore GP was earmarked as the potential starting point given production and transport schedules. At least eight teams had to support the decision.
However, despite promising feedback from testing, in a vote taken during the Monaco GP weekend, a majority opted not to make the change.
"Usually we have some races with rain, like Suzuka, for example," Isola told Motorsport.com. "And it was a good opportunity to test them before the end of the season.
"The problem is that to test them as an additional prototype is difficult because we should send them everywhere in the world.
"I was talking to the FIA, offering the intermediate for Singapore, and then they came back to me saying no.
"The teams didn't agree. Unfortunately, we had more than two teams against, because we needed eight teams in favour."
Isola insisted that he didn't know why teams would reject the new intermediates having accepted the full wets.
"That's a good question. But I don't have an answer, honestly."
Only some teams have been involved in the intermediate testing and Isola acknowledged that others may have wanted to test the new tyres before committing to using them for race weekends.
However, he noted that giving everyone a chance to test them is not practical.
"Clearly, it's also difficult to try intermediate or wets," he said. "It never happened before that we had a full test with all the teams, because you simply cannot organise it."
The rejection came despite the positive outcome of Pirelli's dedicated intermediate testing, with Alpine having conducted the most recent running at Paul Ricard early last month, prior to the vote.
"Esteban [Ocon] was quite happy with the new intermediate step, the step is good step," said Isola. "Without blankets, they were working well, warm-up was good.
"And we tested also in other sessions with different conditions and so on. So in all of these sessions, they have been judged positive, but sometimes it is what it is."
Alpine sporting director Alan Permane confirmed that the new tyres had performed well in the Ricard test.
"We were testing intermediates without blankets and they were really, really good," said Permane.
"Pirelli have done an outstanding job. And we were comparing them to the standard intermediate that was running with a blanket."
Williams team boss James Vowles suggests that while the teams were prepared to accept the blanket-free wets based on data from testing, they were more cautious about voting for inters because they wanted to see how the new wets performed first.
That only happened in Monaco and then more extensively in Canada.
"On the wets, there was some really good evidence that they were working properly, enough running in enough mixed conditions, although all teams hadn't run them in testing," Vowles told Motorsport.com.
"Before we go on the inters, before that decision point, no one other than the teams that had tested had run the extreme wet tyres. Monaco was the first time actually in the race that they were run. And it wasn't perfect, it's a low-energy track in some regard, but it wasn't perfect.
"And the reason why teams would have voted in a cautious manner is let's get some results on track with the existing product, and make sure it definitely doesn't have any ill-sides that we haven't concluded from some specific testing. And you will get that from what happened here [in Montreal]."
