The Dragons have lost all four games during Coleman's tenure as manager, although Levein has also struggled since taking over as Scotland chief in 2009.
The two countries meet in a World Cup qualifying match on Friday, and Brown believes that Levein needs the win more than Coleman.
"The only manager under pressure to be honest is Craig Levein," said Brown.
"I live in Scotland. You see the press there. You hear the supporters. I think obviously with the move [to recall Steven] Fletcher illustrates that.
"The manager [Levein] stuck by his guns and [has] been stubborn for a long time and all of a sudden he has gone back on that. So I think it's quite clear there."
The two sides meet in Cardiff on Friday.