The incident occurred before kick-off when the Northampton squad went for a 'pre-match walk' ahead of the 2-2 draw at Meadow Lane.
Elsnik, who started the game, tweeted: "Went for a pre match walk with the team in Nottingham and this young man outside the hotel started racially abusing some of our lads. The most disgusting thing I’ve seen&heard! He’s done it in front of his girl as well with no shame so he must do it all the time. Absolute idiot!"
Buchanan then tweeted: "Today I witnessed racial abuse to some of our players in the @Village_Hotels in Nottingham! Can’t believe we still have scum like this in 2019! Credit to our boys who handle it impeccably. #kickitout #team @EFL @thepfa."
The club's official account added: "Appalling that our players were subjected to such behaviour today. If anyone has any information please do contact the club."