In the third major assault to hit Britain in less than three months, attackers rammed a van into pedestrians on London Bridge before stabbing revellers in nearby bars.
All team hotels subsequently went into lockdown and the International Cricket Council (ICC) issued a statement on Sunday saying it would review security in line with threat levels.
"It is a sorry state of affairs but we will keep playing cricket and be defiant in the face of it and hopefully put a smile on people's faces here," said Finn, who replaced the injured Chris Woakes in the England squad on Sunday.
"We are fully supportive of the security plans that are in place. We have been briefed on how we are going to be protected.
"We are very comfortable that there is a ring of steel around us so that everyone who is in the ground will be safe. As long as our minds are at ease, we will be alright to play cricket," the 28-year-old added.
Cricket Australia (CA) said they were also "comfortable" with the security for the event featuring the top eight teams in the one-day international rankings.
"We toured Bangladesh last year under very tight security and were looked after very well. This tournament will be no different," Finn said.
Some of his team mates were staying in a hotel less than half a mile (800 metres) from the attack, while all-rounder Ben Stokes was dining in Leicester Square.
"Ben struggled to get back to the hotel because of the roads being cordoned off," Finn said.
"But as far as I am aware no one else was affected or involved. Everyone in our squad was fine."
With Woakes unavailable and Stokes struggling to bowl at full pace because of a problematic knee, Finn can expect to be selected for Tuesday's match against New Zealand with England looking to record a second straight victory in the tournament.
"Woakes is an excellent bowler and has been for England in white-ball and red-ball cricket for a long time. I am obviously taller than the other guys around, so maybe there is a different element to that," he told Sky Sports.
"I'm going into these training days leading in the game and if I get the call beyond that then great and I will try my best for my country."
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
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