Kahn recently said both Schweinsteiger and Lahm were prime examples of how the lack of true leaders on the field is preventing Bayern and other German clubs from being successful in Europe.
Bayern's president Uli Hoeness branded Kahn's remarks "utter rubbish'', while both Schweinsteiger and Lahm have taken exception to his words.
But Kahn told kicker magazine: "Both of them want to and both of them should now take the next step in their development.
"Criticism annoyed me too in the past, but it made me ask questions of myself and that is the kind of attitude I would recommend. I would certainly not have reacted like I had been insulted.''
And the 42-year-old says his career and experience speaks for itself, enabling him to air his views in such a manner.
"If I am asked something, then I give my clear opinion,'' he added. "Maybe Schweinsteiger should actually consider how he can improve in this field rather than reacting so thin-skinned."