Senegal were at their dominant best in Toronto Stadium as they swatted aside 10-man Iraq with style to secure the biggest victory by an African side at the World Cup finals.
Thiaw congratulated his team for getting the job done but struck a measured tone on their performance.
"Even though we scored five goals, there are still improvements to be made," he told reporters.
The West Africans now face an anxious wait to see if they qualify for the round of 32 as one of the eight best third-placed teams. They will know their fate after the end of group stage games.
"Now we have to wait. We have three points secured. There are other matches, so we hope Senegal can qualify," he said.
Senegal are placed third in Group I behind France and Norway.
The coach reserved special praise for midfielder Pape Gueye's hunger and winger Sadio Mane's impact on the team. The former found the back of the net twice.
"He has this team spirit... he does great things on the pitch, he is very helpful defence-wise," Thiaw said of Mane.
Thiaw said he now had peace of mind after the win.
"This country behind us brings a lot, and we give our all to make them happy," he said.
