The German champions took the lead at the Allianz Arena in the Champions League clash, courtesy of a rare goal from Mats Hummels in the fourth minute, but they were pegged back when Noussair Mazraoui found the net for the visitors 20 minutes later.
The Eredivisie champions grew into the contest and looked the more likely to grab a winner as the game wore on, as Bayern's talented attacking players struggled to create any meaningful openings in the final third.
Niko Kovac's men are now without a win in their last three matches and Kimmich is adamant that changes must be made if they are to get their season back on track.
"Things have to change now, we have to do better to dominate our opponents and not be allowed to throw in such mistakes, again and again," the 23-year-old full-back said post-match .
"I do not want to deny the will, it's not about commitment and fitness, it's just that we have too many mistakes in our game."
Kimmich went on to praise Ajax for their display, insisting that they were good value for their point in Munich.
"Ajax did a really good job, they realised that they had a plan both against and with the ball," he added.
"They played really well and were better than us at the beginning of the second half.
"They should have taken the lead, you have to say that we got a lucky point."
Next up for the Bavarians is a home game against Borussia Monchengladbach on Saturday, which is a must-win match for Kovac's side if they are to leapfrog Borussia Dortmund at the top of the Bundesliga table.