The Gunners struggled to create many chances against the Blues, who in turn had 21 shots against the visitors, with six of those efforts on target.
However, Arsenal managed to repel their opponents until the final whistle, leaving the tie delicately poised ahead of the return leg at the Emirates Stadium.
"I felt there was great togetherness, we didn't give many chances away," Wenger told Sky Sports News. "I am pleased with the spirit and determination.
"You want first to be solid, ideally you want to score as well. We were close a few times."
The second leg takes place on Wednesday, January 24, the winner going on to meet either Manchester City or Bristol City in the final.