The midfielder missed out on the first round of games in Sousa's managerial tenure having tested positive for Covid, so Tuesday night's warm-up game ahead of the European Championships was their first international fixture together.
It started well, Klich delivering a beautiful curling ball into the area for Karol Swiderski to tee up Jakub Swierczok who fired Poland into a fourth minute lead.
Russia hit back through Vyacheslav Karavaev volleyed home through Lukasz Fabianski's legs and that was how it stayed.
READ: Klich on his 'place on earth' at Leeds and new role under SousaKlich came off with 20 minutes to go and his boss was pleased with how he fared in the middle of the park alongside Grzegorz Krychowiak.
I really liked the cooperation between Mateusz Klich and Grzegorz Krychowiak," said Sousa.
"They are two different players, but it is important that they do well on the pitch. However, this game and cooperation can be even better and we need to work on it. If they have more time and room to make decisions, those decisions will be better. I also liked the cooperation with Jakub Moder."
Sousa believes Klich's energy, delivery and appetite to get forward and score goals can be vital for Poland in the Euro 2020 campaign, which kicks off on June 14 against Slovakia, before games against Spain and Sweden.
"Mateusz Klich played well, but it can be even better, because that's what football values he has," said the former Benfica, Juventus and Inter Milan midfielder.
"He is a very energetic footballer. He's everywhere. He has a good cross, he is looking for goals and is technically very good. He can determine the strength of the team."