Mexes returned from a four-game ban to feature at the heart of Milan's defence at San Siro and had a hand in both goals scored by the hosts.
The France international won the penalty that Jeremy Menez converted to equalise in the 41st minute.
He then saw his shot from an acute angle give Milan the lead in the 47th minute after it had deflected off Eros Pisano and Panagiotis Tachtsidis on the line.
However, Nico Lopez's strike in the fifth minute of injury time salvaged a point for Verona, heaping further pressure on Milan coach Filippo Inzaghi.
"It's a shame, because it was important to win at home. To concede a goal in the last minute is not nice," Mexes said.
"We have to focus right away on the Fiorentina match [next Monday] and picking up points, because against Hellas [Verona] we dropped two important points.
"I'm really happy to be back playing again after what happened, I'm pleased with the goal and having won the penalty, but it's not enough.
"At the end we lost our way. There was a misunderstanding between myself and [Salvatore] Bocchetti and they scored.
"We must restore winning ways. We are going to Florence for three points. My thoughts are about the team and not my goal, I wanted to do well, but it's not enough.
"We have to pick ourselves up. I cannot be completely happy with the goal because in the end it counted for little."
