The Premier League club progressed to the fourth round of the competition courtesy of goals to Ramires, Loic Remy, Kenedy and Pedro.
The Blues were made to fight for their win over the League One outfit, with defender James O'Connor giving Walsall hopes of a come back victory when he scored in first half stoppage time to make it 2-1.
However, Chelsea's depth of talent overcame Walsall's resilience in the end, much to the relief of Mourinho.
"We were not here to throw away a competition," Mourinho told Sky Sports post match.
"When you start the season with bad results like we did you cannot lose against a League One team. I am always worried with these teams with great belief."
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