The two-time champion headed a thrilling Q3 session at two points, but was pipped on both occasions by Max Verstappen as the Red Bull driver's prowess in the final sector decided pole in his favour.
After his first flying lap in Q3, Alonso felt that he "drove like an animal" to briefly head the session, but had to dig deeper in his second run in his bid to overturn Verstappen.
He reckoned that his efforts were sometimes "over the limit" as he hoped to clinch an all-important pole at Monaco, but addressed the Aston Martin AMR23's weakness in the final part of the lap.
"We were increasing the level to an uncomfortable level of risk, let's say," Alonso, who scored his last pole in Germany in 2012, reflected.
"I think both laps in Q3 were a little bit over the limit sometimes, but everything went fine. The last sector seems our weakest part of the circuit.
"We were, I think, eighth quickest in the last sector. So there is something going on there that we need to analyse a little bit. Maybe going Singapore or whatever is the next opportunity [to address] that."
Alonso explained that it was important to set out his stall early given the propensity for incidents on the Monte Carlo circuit, and was pleased to have achieved a front-row start despite Aston Martin's comparative deficit in qualifying relative to its race pace.
He added that the 78-lap duration of the race would be difficult on the car, and called upon his team to ensure it focuses on getting the race strategy right to stack the odds in his favour.
"You never know here - you know anything can happen here, always a couple of incidents, yellow or red flags, so it's important to put a lap on the board and be at the front," he added.
"With Tsunoda and Max completing their laps, I knew that the possibility was there to be P2. But we were very close to pole position, so we have to be happy.
"We came here with some concerns about our performance on Saturdays, we seem very good on Sundays and taking care of the tyre degradation is very good on, on our work hard, but we're struggling a bit on the street circuit to get the temperature and to put in the heat in our laps in Q3.
"It's a long race. I don't think that overtaking opportunities will come at all, as it's Monaco, but it's a very demanding race on the car, on the gearbox, on the brakes.
"There are a lot of things that we need to take over 78 laps, so we have to be focused and concentrate, and we have to be sharp on the strategy and pitstops."
