Arshavin, who is on loan at Zenit St Petersburg, produced two assists in the 4-1 win in Wroclaw.
" He worked very hard and played very well, " said Advocaat, after his side went top of Group A.
" He is a very important player for us. I am very positive about him. "
Alan Dzagoev scored twice, with Roman Shirokov and substitute Roman Pavlyuchenko also scoring, as the Czechs were well beaten.
With Group A rivals Poland and Greece drawing ۱-۱, Russia have a two - point cushion at the top of the group.
Advocaat ' s side face Poland next on ۱۲ June before meeting Greece four days later.
Yet the former Rangers manager refused to get too carried away despite his team ' s convincing performance and was critical of Russia for not winning by more.
" We are quite happy, we scored four goals and in any international game that is a very good result, " added the ۶۴ - year - old.
" We could have scored more goals, in fact we should have scored more as we had a lot of chances.
" At ۲-۱ we made it very difficult for ourselves so we have to get better at that because maybe a better team would have scored more against us.
" It could have been ۲-۲, there were moments where we need to be sharper, at certain points they had a lot of space and were very dangerous.
" But this was our first game and we are really happy with the result. "
Czech Republic coach Michal Bilek faces a tough task lifting his deflated players before they face Greece on ۱۲ June.
" We had problems with the combinations in Russia ' s midfield and that is how they had so many chances, " said Bilek.
" We are very disappointed but now we have to show our strength and our team spirit.
" We are still able to win and the players have a chance to perform in the following two matches so we are going to look forward now. "
Czech goalkeeper Petr Cech said his team had got carried away.
"There were too many of our players up front and that opened up gaps," said the Chelsea player.
