Coquelin was booked late in the first half of Sunday's Premier League encounter and was perhaps fortunate not to get another yellow before the break, Mason giving the Frenchman the benefit of the doubt following a foul on Wilfried Zaha.
Another challenge after the restart also brought a warning from the official and led to Arsene Wenger withdrawing the 24-year-old as a precaution.
Pardew was incensed by Mason's decision not to issue a second booking, a decision that could have seen a different result.
He told reporters: "I said to Lee Mason: 'Listen. That tackle before half-time is not a sending off at that point but that's his last chance, you know that.'
"He then makes the foul and he [should be] off at that point. Arsene Wenger knew that and substituted him straight away. It's a decision Lee Mason needs to be braver on."
Wenger disagreed with his counterpart but felt that he was left with no choice but to withdraw the midfielder.
The Arsenal boss remarked: "I felt he was not fortunate. I would like to see that again but, in the end, the pressure created by the crowd meant I took him off.
"When you are 2-1 up and he is playing quite well, that's difficult. It's a sensitive decision."