The Arsenal manager saw his team surrender a 2-0 advantage as Wolves struck in stoppage time to earn a point.
Arsenal had moved into control through goals from Bukayo Saka and Piero Hincapié, before Hugo Bueno pulled one back with a long-range effort.
In the closing moments, goalkeeper David Raya spilled a shot and Riccardo Calafiori was unable to prevent Tom Edozie’s effort from crossing the line.
The result denied Arsenal the opportunity to move seven points clear of rivals Manchester City, who can now close the gap to two points with victory over Newcastle United before Arsenal face Tottenham Hotspur in a north London derby.
Speaking after the match, Mikel said: “Very tough to accept it. In the second half we did not perform in the way we should and the way we require to win a Premier League match.”
He added: “It is better not to judge it, we are all too emotional about it. You have to take the hit because we deserve it. It is very easy with emotion to say things that can damage the team.
“Everyone wants to do their best. You have to go through tough periods. Today at the last minute, we paid the price. We have to do basic things much better than we have done.”
Asked why Arsenal were failing to capitalise on dominant positions, Mikel said: “Today we need to accept it. We need to be critical of ourselves because it was not good enough. In the league, it is the reality that we have not been consistent over the last few months.
“You have to stand up. When you have a moment of difficulty, we have to show how much we want it and how good we are. We have to stand up.”
Bukayo was equally critical in his post-match interview with Match of the Day.
He said: “Disappointed. Not much else to say. There was a big difference in how we played in the first half and the second half. We dropped our standards and we got punished for it.
“Time to focus on ourselves, improve our standards and improve our performances and it is in our control.”