Spurs had beaten Dyche's side 5-0 the day prior at Tottenham Hotspur Stadium.
Dyche stayed in London for an extra day and bumped into Mourinho.
"I'll tell you a little life story," Dyche said on Thursday. "Strangely, after a bad day for us, a bad result that's for sure, the next day, with eight–odd million people in London, I bump into Jose Mourinho!
"That was a strange moment for him and me. But we were both correct because he said they were very good, which they were, and I said we weren't, so we were both right. Anyway, it was just a life moment, that I thought was quite interesting.
"I spoke to him more than I have before, ever. We had a good 10 minutes, and he was very polite, very kind to my family. It was an interesting moment in a city of eight-odd million people.
"I was on my way to Poundstretchers by the way – he was on his way to Harrods!
"His face was actually more shocked than mine, because he was plodding along and I saw him with his hat on, and he shot his head up and said a bad word, and then said, 'Sorry, your wife and children are there!'
"But he was very pleasant – as he would be after smashing us the day before. But we had six or seven minutes chatting about how he's settling, life in general, that sort of stuff. But he was very pleasant."