The 41-year-old seven-time world champion ended up third on the grid after being outpaced by four-time champion Max Verstappen of Red Bull and then, on the final lap, championship-leading Italian teenager Kimi Antonelli of Mercedes.
His Ferrari team-mate Charles Leclerc qualified fourth, but smacked the barriers as he pushed for an improved lap in the final seconds.
"It was tough for us," said Hamilton.
"We were looking so strong in practice and we barely changed anything, but the car was drastically different once we got to qualifying for some reason. So, we have to take a deep dive into that.
"I gave it absolutely everything and I was as close to the barriers as I could be - and what a privilege it is to be here, to be one of the 22 drivers in F1 getting to do this still. I love every second of it!"
He added: "It is definitely very close between us all. I thought we almost maybe nearly had it and then Max put in a good time and then Kimi! I think it’s great to see how close all the cars are - but we are there in the fight."
Since 2006, the pole position starter has won 13 of the 20 races at the Monaco Grand Prix, but this year's new 'hybrid era' formula has seen cars on the second row of the grid take the lead at every race on the opening lap.
