“I think these people would have us stay in our houses, locked up 24 hours a day if we let them have their way,” Coleman told BBC Radio 5 live. “That shouldn’t happen.”
He said he expected Euro 2016, which starts in France on 10 June, to be “incredibly secure” and said he was confident Uefa, European football’s governing body, would do its “utmost” to keep everyone safe.
But the former Fulham and Coventry City boss added: “If somebody’s hell bent on walking into a crowded area and they want to blow themselves up or whatever, there’s only so much security can do.
“There’s always going to be a doubt in everybody’s mind. You’re hoping and praying that everything’s going to be OK.
“We’ve all got to go there and try to enjoy the tournament, try to entertain everybody that’s going there as best we can.”
Suicide bombers struck near the Stade de France in Saint-Denis, followed by suicide bombings and mass shootings at cafes, restaurants and a music venue.
The attack on the Stade de France took place during France’s football friendly with Germany, with radio and television teams inside the venue capturing the noise of the bombs going off outside.
Following the game, the German players slept in the stadium to ensure they remained safe before travelling home.
So-called Islamic State (IS) has said it was behind both the Paris and Brussels attacks.
Norwich City striker Dieumerci Mbokani was at Brussels airport when the explosions occurred. According to his club, he was “unharmed but shaken”.
It is thought the player was there in order to fly to Kinshasa to join up with his DR Congo team-mates for an Africa Cup of Nations qualifying double-header against Angola on Saturday and next Tuesday.
Belgium defender Vincent Kompany, who plays his club football in England for Manchester City, said he was “horrified and revolted” by the attacks, tweeting that “innocent people were paying the price again”.
International team-mate Christian Benteke, who plays for Liverpool, said his thoughts were with family and friends of the victims.
People in Brussels and surrounding areas have been told to avoid rail stations, airports, shopping centres, concerts and other public events following Tuesday’s events.
But organisers of the Dwars Door Vlaanderen say the one-day cycling race across Flanders will proceed as scheduled on Wednesday.
A statement on the race’s website read: “Dwars door Vlaanderen will take place. The organisers mourn with the victims of these terrible acts.”
Britain’s Scott Thwaites, who will be riding in the race for Team Bora-Argon 18, told BBC Sport that security was “a concern”, given the size of the crowds and the proximity of fans to competitors.
“That is the beauty of cycling, that when you are riding around the country there are fans everywhere on the roadside creating a great atmosphere,” he said. “I would not like that to change.
“Everyone is doing their best and we have to keep the show on the road.”