Arsenal came from behind to beat the resilient Eagles with goals from Laurent Koscielny and Aaron Ramsey, the latter coming in the dying minutes of injury time.
Arsene Wenger's men were by no means at their best against Palace, but Nicol singled out the £35 million man for some intense criticism.
"Sanchez was awful," Nicol told ESPN FC.
"His delivery, whether it was from set pieces or actually from a rolling ball, was horrendous. It was either too long or too short or too high, he just never, never got one right."
"But you would have to say he is going to have a bit of a World Cup hangover."
Sanchez started strongly in his league debut, regularly running at the back four and causing Crystal Palace problems.
He seemed to grow frustrated and tired late on as the Gunners struggled to break down their opponents, and his crosses began to lose their precision, which is what Nicol is alluding to.
The Chilean certainly got one delivery right, however, contrary to the former Liverpool man's view - his pinpoint cross from a free kick set up Laurent Koscielny's equaliser late in the first half.
Sanchez may not have been at his best in his first Premier League game, but with an assist and some real flashes of brilliance he showed plenty of promise for the season ahead.