Christian Today reported that Most Revd Peter Smith was speaking at St George's Cathedral during its annual Mass for Migrants on Monday.
He warned about the dangers faced by young people in the world's poorest nations and highlighted that they may fall victim to traffickers.
He said: "Nor can we close our ears and eyes to the dreadful tragedy over recent months of hundreds of migrants drowning in the Mediterranean, fleeing from persecution and abject poverty and heading for Europe in over-crowded and unseaworthy boats."
The Archbishop also spoke of the fate of those arriving in the UK.
He referred to a recent report from the all-party parliamentary group on migration, which found weaknesses in Britain's detention and removals policies.
He added that the current system is "seriously detrimental to the individuals who are detained in terms of their mental and physical well-being, effectively stripping them of their human dignity and respect."
There are "no easy answers" to the problem of how to balance the needs of residents with those of migrants, he said.
"We must pray for our politicians and our government, both national and local, and whilst we have the right and the duty to hold them to account, we should always do so with courtesy and respect."
Ambassadors from Libya, Ethiopia and Lithuania attended the Mass and the service featured music from all around the world.
