The 24-year-old recently joined the Eagles from Newcastle United after the London club activated a £13m release clause in the winger's contract.
Manager Alan Pardew gave Townsend an hour to impress, but he and his teammates failed to get off the mark as the match, which is part of the club's US tour, ended in a stalemate.
For the majority of the first half, Palace had to work off the ball as the hosts had plenty of possession, but goalkeeper Julian Speroni was rarely troubled.
The visitors came close to scoring numerous times through striker Freddie Ladapo, but his final touch failed to steer the ball into the back of the net.
Summer signing James Tomkins, who joined Palace from West Ham United, made his debut in the second half, and almost converted a header past the goalkeeper, but he narrowly missed the target.