The only major defeat during the first invasion of Europe I ever heard about was the Battle of Samara Bend, battle in which Subutai is only alleged to have taken part directly, and which happened just before the main invasion of Europe. Took a quick look at it and there doesn't seem to be many sources about the exact forces and losses at stake. They were pretty much considered undefeated during the first invasion of Europe until they retreated in 1242, for reasons still disputed (death of Great Khan (very disputed, search for "According to John of Plano Carpini" in that great article), little gains from costly battles, bad winter, etc.).

The first significant defeat of the Mongols in the West is considered to be the battle of Ain Jalut, which happened in 1260 close to Jerusalem, long after the first European invasion which ended almost 20 years before (and wasn't led by Subutai who died in 1248, 12 years before).

As it was, the Mamluks not only stopped the Mongols’ westward advance, but—just as important— they also smashed the myth of Mongol invincibility. The Mongols’ belief in themselves was never quite the same, and ‘Ain Jalut marked the end of any concerted campaign by the Mongols in the Levant.

After this there are many records of significant losses from Mongols in Europe, but this gets a bit too much off-topic :) (Battle of Łagów in 1287 during 3rd invasion of Poland for example)