Dzeko was a consistent if unspectacular performer during four-and-a-half seasons at Manchester City, scoring four goals in 22 Premier League appearances in his final campaign before joining Roma in 2015.
After a sluggish first season, the 30-year-old has scored 20 goals in 29 appearances in all competitions this term, though he retains a reputation for wasting too many chances in front of goal.
"In England there was less pressure. If you do not play well it is normal that they criticise you. But criticism is part of the game, so you accept it," Dzeko told Il Messaggero.
"At Roma it's similar to with Bosnia, they do not criticise you, they insult you. So I'm used to it.
"At home, you will be OK if you miss three times, but a fourth and the insults start again. It's as if they are waiting for the right opportunity to hit you.
"I can just remember what I have seen and then I often think about how I do well throughout the match and then if I miss one chance, everyone talks about the miss. Only that."
Dzeko has enjoyed the greater work ethic that coach Luciano Spalletti has instilled since taking over from Rudi Garcia a year ago.
"[Garcia] needed to be a little harder on us, just like Spalletti is. You have to avoid someone who relaxes you too much," said the striker.
"Spalletti wants more and more from me and the whole team.
"So I would like to hear from him every now and again, for him to give me a compliment to know I have done well.
"But I have nothing against Spalletti. I want to do more and more, it provides me with an incentive.
"Spalletti believes a coach must let players know who's the boss. Spalletti always wants to win and this is positive for the team.
"At Roma it's not easy; if you win three games you've won the league title, if you lose one, everything is bad."