Mourinho, who signed a new four-year contract in August, lead his team to a domestic double last season, adding the League Cup to the Premier League title.
However, with just 11 points from 11 league games, Chelsea are languishing down in 15th place in the table, 10 points behind fourth-placed Manchester United.
Saturday's sixth league defeat means Chelsea have already lost twice as many Premier League games than they did last season, a statistic compounded by just one victory in their last eight games in all competitions.
Mourinho's problems are not confined to the playing field, however, as the 52-year-old was charged with misconduct by the English Football Association (FA) after being sent to the stands in the West Ham loss and is currently appealing a 50,000 pound fine imposed for criticising referees.
With his manager's future as uncertain as ever, Mikel has voiced his backing for Mourinho and is confident the Portuguese is the right man to turn things around.
"The goals and wins are not coming but you can see we are playing for the manager and are right behind him. There is no doubt about it. If anyone can turn this around, I definitely think he is the one," Mikel told the club website.
"If you say to the players that we are not giving 100 percent then there is a doubt -- but we are giving 100 percent, we are playing for the manager and we are right behind him, the Nigerian international added.
"Everyone can see how much hard work we are putting in and we are playing well but the results are not coming for us.
"Every shot (against us) is a goal, every deflection a goal. We just need a bit of that luck that we don't have at the minute. But you can see the team is giving it everything, we're working very hard," he added.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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