Mourinho did not take kindly to past comments made by the younger of the siblings, who claimed that it was a "pity" the English youngster plied his trade under the Special One.
The United boss hit back by describing Frank as the "worst manager in Premier League history" following his failed spell with Crystal Palace at the start of the season, but Ronald has attempted to play down the spat before it gets too personal.
"Managers have different philosophies when developing young talents," he told Sky Sports News. "Not right or wrong, simply different, and you have to respect that. Mourinho bought [Alexis] Sanchez in January and of course it's the truth that it's not good for Rashford's development and he will play less now for Man United.
"Rashford is without doubt one of the biggest talents in the Premier League and could play a big part [at the World Cup] in Russia this summer.
"Frank respects Jose a lot and was simply pointing out that, if Rashford was playing for Ajax and had one or two bad games, he would still start the third game. However, he's at Man United and after two bad games things are different and he'd be on the bench."
Rashford started his first Premier League game since Boxing Day on Saturday, scoring twice in United's 2-1 win over arch-rivals Liverpool.