Lewandowski scored twice and Bayern secured top spot in Group E with a thrilling 3-3 draw in Amsterdam, with both teams reduced to 10 men.
Bayern twice led and yet twice let their advantage slip, including in stoppage time when Kingsley Coman's late strike was cancelled out by Nicolas Tagliafico in the 95th minute.
While Bayern progressed to the last 16 as group winners, Lewandowski – who ended the phase as the leading scorer ahead of Lionel Messi with eight goals – was not satisfied.
"That was a very offensive game," the Poland international said. "But what we showed in the possession game wasn't good. That was missing.
"Ajax had more ball possession. We still had a lot of opportunities, but we didn't use them.
"[Ajax goalkeeper Andre] Onana also did a great job. We have a lot more potential."
Bayern were reduced to 10 men in the 75th minute after Thomas Muller was shown a red card for a high boot, his departure coming just eight minutes after Maximilian Wober's dismissal left Ajax a man down.
Bayern goalkeeper Manuel Neuer added: "It was very interesting at the end. There was a lot of fight and passion in it.
"Ajax are simply good, we have already seen that in Munich. The most important thing is that we are first."
Bayern sporting director Hasan Salihamidzic was candid in his assessment of the match, despite the club finishing top of their group.
"The only positive thing is that we are first," Salihamidzic said. "We didn't make a good game, we gave the game away completely, it can't be."