The Frenchman believes the Serie A representatives were in control throughout the game and fully deserved victory
The Scottish champions created a number of good chances to open the scoring, but failed to beat Christian Abbiati and were eventually punished for their profligacy as an own goal from Emilio Izaguirre and a Sulley Muntari tap-in helped the Rossoneri to victory.
"I don't think we suffered that much to be honest. We controlled the game well and finally managed to score in the final minutes," Mexes told the official Uefa website.
"I don't think Celtic had so many opportunities – they had a couple of shots on goal but they really didn't trouble us. We controlled the game and finally scored when we had the chance.
"It was important to get the points tonight as it was crucial to start the group with a win. We needed it especially to regain some confidence after our last match against Torino when we did not play well.
"Despite missing several players due to injuries, we proved that Milan have a big heart and now we can start focusing on the game against Napoli in good spirit.
"The next fixture against Ajax is important too, but all the matches are decisive in this group. We will try to play well in Amsterdam and come back to Milan with some points."
Milan clash with Ajax on October 1 at the Amsterdam ArenA.