With United searching for a breakthrough at Selhurst Park on Wednesday night, Maguire fumed at Rashford after he was caught offside, telling him to ‘f****g stay onside’.
Rashford immediately snapped back at his skipper, telling him to ‘shut the f*** up, f*****g nobhead’.
But Maguire insists the incident was ‘nothing’ and something that happens frequently behind closed doors on the training ground.
The draw in south London saw Manchester United lose further ground on Premier League leaders Man City, who they face on Sunday afternoon.
‘You pick up these things as there is no crowd in the stadium,’ Maguire told The Sun. ‘But we are always shouting at each other in games.
‘I have full respect for Marcus and he has full respect for myself. We did not even confront each other after the game because it happens that much in training and in games.
‘He wants the best for the club and I want the best for the club. We were not winning and late on in the game were both a little bit frustrated but no, it is nothing.
‘It just shows we are going in the right direction. We are passionate. We are frustrated.
‘We want to be winning football matches. We are passionate about the club and team spirit. We show passion.’
Maguire added that it is important for players to be vocal during matches as it shows they are leaders.
‘If we want to win titles and win trophies, we must have leaders,’ he said. ‘We are starting to get that.
‘We are vocal on the pitch. Listen to the players and we are the loudest in the Premier League.
‘We do speak about having the right mentality. If you do not have the right mentality, you’re at the wrong club. As a group, we speak about leadership, mentality and focus.
‘When you talk during a game you can keep your own focus and help organise the team.’