Shares fell more than 1 percent in extended trading, and Adami believes they will slip even lower.
"The stock is in a lot of trouble right here," he said.
Read MoreAmEx earnings: $1.48 per share vs. expected EPS of $1.37
The after-market move sent American Express below $80 per share. Adami believes it can slide below $77 per share.
However, trader Brian Kelly said he would buy the stock at its current level. He noted that American Express card spending rose year-over-year and the dollar reversed course against a basket of global currencies on Thursday.
Visa and MasterCard are more appealing credit-card plays, trader Steve Grasso noted. Both names closed slightly lower on Thursday.
Tim Seymour is long T, BAC, BX, C, DAL, DIS, F, GE, GM, GOOGL, INTC, EWP, SUNE and TWX. Tim's firm is long BABA, BIDU, IBN, MCD, NKE, NOK, SBUX and VALE. Today, his firm sold YNDX. Today, his firm bought VALE.
Steve Grasso is long AAPL, EVGN, MJNA, PFE, T, TWTR, GDX, BAC and BTU. His firm is long AMD, AMZN, NE, OXY, VALE and RIG. His kids own EFG, EFA, EWJ, IJR and SPY.
Brian Kelly is long BTC=, euro, GLD, EEM, CTRL calls, GSG, BBRY and SPY puts. He is short U.S. dollar. He is short 30-year bond futures. He is short yuan. Today he shorted 30-year bond futures. Today, he sold TLT.
Guy Adami is long CELG, EXAS and INTC. Guy Adami's wife, Linda Snow, works at Merck.