Lahm is just 30 but has decided to call time on his Die Mannschaft career after leading his country to World Cup glory in Brazil this summer.
Schweinsteiger and Lahm have played alongside one another for Germany for a decade and he is sorry to see his Bayern Munich team-mate go.
"It's a pity, we always had a very, very nice time in the national team, he is a world-class right-back - if not the best in the world," the midfielder told reporters.
‘We are there to find a solution, but it's a shame. I was hoping to play some more games with him.”
Schweinsteiger would appear to be one of the most qualified candidates to succeed Lahm as Germany skipper, but he is playing down his chances of being given the captain's armband by Joachim Low.
“We have many players who can be captain," he mused. "The coach decides.”
Schweinsteiger’s club and international team-mate Manuel Neuer spoke of his own chances of inheriting the captaincy, but the goalkeeper is calm about his prospects.
"If Jogi Low speaks to me, I would first talk to him," the goalkeeper admitted. "If it is concrete, I will prepare myself.
"It is a decision that you do not have to make now because talks will come. Then, at some point, a decision will be made."