Short answer. No. Article 1918 excuses the principal from liability for expenses the agent incurred when those expenses were due to the fault of the agent — so expenses caused by your agent's own mistake are not something you are obligated to reimburse.
What the law says
When the expenses were due to the fault of the agent
Civil Code, Article 1918 — When the Principal Is Not Liable for Expenses. Read the full provision →
The rule that answers your question directly
Article 1918 lists four situations where the principal is not liable for the expenses incurred by the agent, and the second is exactly your situation: when the expenses were due to the fault of the agent. If the agent's own mistake, not yours, is what caused the expense, this clause squarely removes your obligation to reimburse it, since the expense traces back to the agent's own conduct rather than to anything you did or authorized.
Acting against your instructions is a separate exception
The same article also excuses reimbursement if the agent acted in contravention of the principal's instructions, unless the latter should wish to avail himself of the benefits derived from the contract. This covers a different scenario from fault — an agent who simply disobeyed what you told him to do — though a principal who chooses to keep the benefits of that disobedient act may still end up owing for it.
Expenses incurred knowing the result would be bad
A third exception applies when the agent incurred them with knowledge that an unfavorable result would ensue, if the principal was not aware thereof. An agent who pressed ahead knowing the outcome would likely be bad, without telling you, cannot then expect reimbursement for the expenses that produced that outcome — the exception is meant to discourage an agent from keeping the principal in the dark about a foreseeable problem.
A fourth exception: what the contract itself says
Finally, the article respects whatever the agency agreement itself provides: when it was stipulated that the expenses would be borne by the agent, or that the latter would be allowed only a certain sum. If your agreement with the agent already fixed who bears certain expenses, or capped what would be reimbursed, that stipulation controls regardless of fault, since the parties are free to allocate expenses between themselves however the agency contract provides.
What this means for you as the principal
Because your agent's expenses trace back to his own mistake rather than to your instructions, your knowledge, or anything you stipulated, none of the four exceptions in Article 1918 works in your favor to expand liability — the fault-of-the-agent clause simply removes the reimbursement obligation for that expense outright. Keeping a record of how the expense arose, and whether it was genuinely the agent's own error, is useful if the agent later disputes that characterization.