Marcos Alonso scored the only goal of the encounter in first-half stoppage time in a game that saw the Blues register 24 shots - and eight on target - but fail to put the result to bed.
The result did mark the reigning Premier League champions' fifth consecutive league win, however, and saw them move level on points with Manchester United in third in the table.
"When you do not score the second goal, you have to suffer," Conte told Sky Sports News afterwards. "You are afraid at every corner and free kick and the opponent has the chance to draw. We dominated the game, shooting 24 times, hitting the post and we needed to score the second goal to be relaxed.
"We had a lot of chances but the goalkeeper Fraser Forster was good. We have to be happy with the performance and the clean sheet.
"If you shoot only twice and score two goals, you must be worried. We had lots of shots but we must be more accurate in our finishing.
"In the last 10 games, we have won eight, drawn one and lost one. This is our run, you have to consider last 10 games, not just two. It shows we are doing our job."
Next up for Conte's side is a home encounter with Bournemouth in the EFL Cup on Wednesday night, ahead of a trip to a resurgent Everton next Saturday.