They made the worst possible start, going behind after only 45 seconds when Mickey Demetriou scored with a left-foot shot after a cross from Scott Twine found him unmarked.
Substitute Padraig Amond added a second a minute before half-time after Tristan Abrahams played the ball into his path and former Bradford player Matty Dolan scored from the penalty spot in stoppage time after Connor Wood brought down Twine.
It made a happy return to Valley Parade for Newport manager Michael Flynn who was signed by McCall in his first spell as City manager and played for the club for three years between 2009 and 2012.
“Michael Flynn has done an excellent job,” said McCall. “Their players have been there for two or three years and they are a very strong side. They have confidence and momentum.”
McCall changed the team’s shape at half-time, and said: “We got into some dangerous areas in the second half, but Newport are difficult to break down. We have to do better in the final third.
“It is a mental as much as a physical challenge for us at Bolton. We were beaten by a really good side, but that doesn’t make any excuses for our poor performance. We are looking for a better performance at Bolton.”
Bradford City: O’Donnell, French (P O’Connor 45), A O’Connor, Richards-Everton, Wood, Watt, Cooke, Clarke, Samuels (Mottley-Henry 45), Novak, Guthrie (Donaldson 65), Unused substitutes: Hornby, Longridge, Pritchard, Cousin-Dawson.
Newport County: Townsend, Shephard, Cooper, Dolan, Demetriou, Haynes, Sheehan, Labadie (Bennett 64), Twine, Abrahams (Proctor 83), Janneh (Amond 42). Unused substitutes: King (gk), Baker, Willmott, Ellison.
Referee: D Bourne (Nottinghamshire).
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