The double F1 world champion finished 17th in Q1, four tenths behind Alpine team-mate Esteban Ocon, who did go through to Q2 and qualified 11th.
Alonso said his team has question marks over its lack of pace in the streets of the principality after showing improved form in Portugal and Spain.
“There’s still some question marks I think for the team to find out,” Alonso said.
“I think in Portugal and Barcelona we were definitely progressing and being quite competitive while here we were quite down on the times, so it’s still a little bit under investigation.”
PLUS: How box office Alonso is still proving his star quality in F1
Despite being outqualified by Ocon in the past four races Alonso played down suggestions he was lacking confidence in the car.
“No, I think the confidence was good,” he added.
“I was able to push the car and extract the maximum. It’s always a bit messy in Q1 with traffic and things like that, that was not ideal.
“But I don’t think that was the cause of being out of Q2, we didn’t have the pace.
“I think the whole weekend we’ve been struggling a little bit with the pace.
“We were expecting more from Monaco on our package, but we didn’t deliver.
“The race is going to be difficult starting at the back, no doubt. But let’s see what we can do.”
Fernando Alonso, Alpine F1
Photo by: Mark Sutton / Motorsport Images
Executive director Marcin Budkowski explained Alpine is struggling to get the most out of its Pirelli tyres this weekend, which left the Enstone engineers “scratching our heads”.
“It was not a good weekend overall for us and unfortunately it’s not really getting any better,” Budkowski said to Sky Sports F1.
“We’ve struggled to get the tyres to work all weekend, and I think that’s still the case for Fernando.
“That’s the tricky bit about these tyres. I think some cars, like the Ferraris, just seem to get them to work properly and some cars struggle more.
“And quite often the ones that switch them on quicker are the ones that wear them also quicker. It’s a difficult balance to get.”
Budkowski revealed Ocon was in the same boat as his team-mate throughout the weekend but managed to get his tyres to grip up at the end of Q1, yielding a time that was comfortably quick enough to progress.
“We’ve been scratching our heads, and had some simulator running yesterday to try to get it right,” he explained.
“Interestingly Esteban, for the first time, his second run in Q1, started to feel the grip from the tyres.”