The 20-year-old, who was set to spend the rest of the season with Sam Allardyce's men, returned to Anfield earlier this month with only a single appearance for Bolton to his name.
Otsemobor was quick to make clear his disappointment upon returning to Merseyside, but Brown feels that any player must earn the right to be in contention for a starting spot.
Brown said: "The only gripe Jon could have, would be his lack of first team opportunities.
"He came to us with six or seven games under his belt at Liverpool and probably had an idea that, looking at the relative successes of the two clubs, he should be able to play in our first team.
"But that theory could not be any further from the truth. You've still got to prove yourself, regardless of who you are playing for, and whether you are Jon Otsemobor or Steve Howey."