Aberdeen keeper Brown, 30, was handed a starting role with Wayne Hennessey, Boaz Myhill and Lewis Price all unavailable through injury. While he was beaten by two close-range finishes from Aldo De Nigris, Brown also pulled off a string of excellent saves.
Coleman said: "He did great, he was fantastic. We try to build from the back, and that means that sometimes the keeper has a lot of the ball and not too many like to have the ball at their feet for too long. Throughout his career he has not been asked to do that and he did a great job. He is a cracking lad, a real nice guy and a good professional."
The stand-out stop was a brilliant save from the excellent Giovani Dos Santos' point-blank header, while he also made sharp blocks to deny Edgar Andrade and Severo Meza.
Coleman admitted Brown, winning his third cap over five years after his second, could not have done any more to impress with his all round display.
He said: "He has worked very hard, he made some great saves and distributed well. Credit to him because it was difficult for him to come in at the last minute with Hennessey, Myhill and Price missing."
Those difficulties were added to by the oppressive heat and humidity of the mid-afternoon kick-off, and a lifeless playing surface at the home of the New York Giants and New York Jets NFL teams.
He said: "It was a tough game for us, Mexico are a super team, they play with imagination and move the ball well. Teams don't come much better than Mexico but we gave everything we had."