The Aston Martin driver finished second to Formula One championship leader Verstappen, who has now won at Zandvoort for three years in a row and is also on a record-run of nine successive wins, in the rain-affected and red-flagged race.
“This is a very special racetrack, with all the fans and the energy going on, so you feel always very focused,” the Spaniard told reporters.
“I did think about trying a move in the last restart but then I thought maybe I cannot exit the circuit so I stayed calm in second.”
A crowd of 105,000 packed the seaside circuit with 305,000 over the three days of an event that has become a celebration of Verstappen by his lively orange army of fans partying through the weekend.
Verstappen had no easy ride on Sunday, with rainstorms early and late in the proceedings making it the sort of race where any mistake could prove extremely costly.
Alonso, also a double world champion, started fifth on the grid but had passed Mercedes’ George Russell and Williams’ Alex Albon by the third corner with a bold move on the inside.
“It was one of those Sundays where you feel connected with the car, you feel in sync with the car, and everything you do, the car is just answering perfectly,” said Alonso.
He had appeared on the podium six times in the first eight races of the season but Aston Martin had lost their momentum in the last four with the Spaniard no higher than fifth as others improved.
Sunday was a return to that early season form and Alonso, the most experienced driver on the starting grid, made the difference with a lesson learned earlier in the weekend.
“It was wet (in practice) and in one of the out-laps I let a few cars go on the normal racing line and I found a lot of grip on the inside casually, by just letting people go,” he told reporters.
“So, I kept in my head, all the time, all the weekend, in case it was wet. I was ready to try again…I thought about the inside line, it could work and we overtook those two cars.
“Definitely, that should be the overtake of the month, again. I hope.”
(Writing by Alan Baldwin in London, editing by Toby Davis)