The Blues midfielder thanked the on-loan Atletico Madrid goalkeeper for his contribution in a difficult first half during their 2-0 win over Macedonia FYR in Skopje on Friday
The 20-year-old Chelsea goalkeeper has spent the last two seasons on loan at Atletico Madrid but is expected to succeed Petr Cech as the number one at Stamford Bridge in the near future.
Hazard was impressed with the young shot-stopper's display on Friday while admitting that Marc Wilmots' side encountered problems early on in Skopje.
"It was just like the game against Serbia. We had trouble in the first half but in the second it went a lot better for us," he told reporters.
"The match was not easy. Courtois kept us in contention with a few good saves using his leg. I didn't think I played too badly, but I can always do better."
Meanwhile, Manchester City defender Vincent Kompany feels everyone put in a fine performance in his absence, and was happy that his team gave the fans what they deserved for making such a long trip.
"A great result, the men played perfectly. I am pleased that we can give so much to our country," he wrote on Twitter.
"Our fans have made a long trip to Skopje and they have been rewarded. Massive thanks for the support."