Alonso finished second in a rain-affected and red-flagged Zandvoort race, 3.7s behind home hero Verstappen in the Red Bull.
When the race restarted with six laps to go after a long delay for a break in the weather, Alonso considered making a lunge on Verstappen into Turn 1, but he joked he thought better of it as he would have risked taking the Dutchman out and "not being able to exit the track".
"I did think about trying the move on the last restart but then I thought maybe I cannot exit the circuit, so I stayed calm in second," Alonso joked, referring to the sea of orange Verstappen supporters in the grandstands whose party he would have spoiled.
"The energy in Zandvoort is very unique. When this race came [on the calendar] I thought I would never experience a Zandvoort podium because I was not in a position to think about that. And today is going to be very special to share the podium with Max and Pierre [Gasly, third]."
It was a return to form and to the podium for Alonso and his Silverstone team after a spate of more difficult races before the summer shutdown.
During a turbulent opening phase, Alonso climbed from fifth to third, later moving up to second after the other Red Bull of Sergio Perez went off the road just before the red flag came out on lap 65.
After the finish, Alonso even told his team on the team radio: "We will win a race soon, we are getting closer."
But until then the 42-year-old Spaniard was satisfied with netting his seventh podium of the campaign thanks to a car that was "flying" in the Dutch dunes.
"It was a very, very intense race with the beginning in wet conditions," the two-time world champion added.
"We were very fast and we stopped maybe one lap too late but the same as the leaders.
"The car was flying today, very competitive, very easy to drive. In these conditions, you need a car that you can trust.
"And I did trust the car a lot today, so I enjoyed it."
