Yes, Jesus did say this (John 14:6). However, perhaps he meant that he will judge as to who enters eternal life - heaven - and maybe that includes those who worship the one true God. Or, even those who through no fault of their own are of other faith - or no faith. He also said that he had sheep not of this fold. I think we should be slow to judge others lest we be judged, as Jesus also said. He also said something about casting the first stone.
There are millions of Christians, including wonderful Catholics, who are ready to dialogue with and respect other faiths. I can't believe for a moment that Christ would be against this. My God certainly is a loving deity who is slow to anger and understands all the impulses, ignorances, and aspirations of his vulnerable, earthly children.
My guess is that this particular priest said that the word of God could be found in the Koran (Qu'ran). There is some truth in this. Frankly, I find evidence of God's word in the scriptures of many faiths. St. Paul tells us this.
In any case, he must be both a learned and empathetic priest. We need more such perceptive and open-minded clergy of every religion to help cure this world of its narrowness and bigotry. Again, God bless him and bless all humankind, of whatever race, creed or color.