Owls captain Purse was criticised by his manager Brian Laws over Derby's first goal and the summer signing from Cardiff was also involved in a heated exchange with Grant after Lee Croft had capitalised on some indecision in Wednesday's defence to fire the home side ahead.
Grant told the club's official website: "I think of late we've conceded too many goals and as a goalkeeper I take that to heart.
"I'm very likely to get upset and irate. That's part and parcel of it, it happens on a football field.
"We've not fallen out, certainly not. He's a good lad. He's the skipper at the end of the day and anyone not clued in can expect to have a few stern words now and again and he's no different.
"But we kissed and made up. Like I say, it's part and parcel of it. Everybody has their opinion on how things should go and it's a case of trying to get everybody going."