Cardinal Vincent Nichols said Britain's response to the crisis was "going very slowly" and called for a major increase in the number of people being taken in.
Prime Minister David Cameron has agreed to take 20,000 displaced people from camps in the Middle East over the next five years, far fewer than other EU counties.
Cardinal Nichols said he believed the government had to show more humanity.
He told BBC Radio 4's Today programme: "I think we have the resources as a very rich country. Think of a country like the Lebanon and some of the other Middle Eastern countries where they have a proportion of refugees present which represents 30-40% of the population and they cope.
"We are a very rich country and I think with a greater cohesiveness between a spirit of willingness that is there among many and mechanisms which governments can put into place, we could be doing more."
He added: "There are aspects of the government policy that are commendable but I've said surely that can be speeded up. Surely in the first year we can see really how many could be taken and then multiply that by five.
"At the moment it's going very slowly and it's a great disappointment."
Cardinal Nichols dismissed suggestions that the UK should not be taking in refugees because some Britons are struggling to make ends meet.
He told the programme: "I don't think the struggle of people in the destroyed villages in and around Mosul and other parts of Syria, those struggles are not the same as our struggles."
He added: "They are people like ourselves and they are desperate and we should open our hearts as well as our political and financial resources."