The Leeds United midfielder failed to feature in his country's 2-2 friendly draw with Iceland on Tuesday night, remaining on the bench for the duration of the match.
Klich completed 70 minutes against Russia last week - setting up Poland s opener in another draw which ended 1-1 - but wasn't called upon by boss Sousa in midweek.
The 30-year-old was given special dispensation by Whites head coach Marcelo Bielsa to head away on holiday early for a much-needed rest ahead of the conclusion of the Premier League campaign.
The early departure from Elland Road was a bid to help prepare Klich for this summer's delayed Euros tournament which kick-off on Friday.
"We decided on two forwards to open the centre and play by the defenders," Sousa explained of his team selection on Tuesday.
"We have to help Robert Lewandowski more consistently, we have to provide him with more balls so that he can do what he does best: score goals."
Asked about Klich and why he was absent, he said: "Yesterday the doctor showed us the players we should spare. That is why we decided not to play [Mateusz] Klich.
"Some played very well; especially in a one-on-one situation. However, we have to be much more dangerous on the left side.
"In the first half, the low play was much better. There was a lack of speed and frequency of plays, but it was dependent on the behaviour of the rivals.
"We tried to play forward, move faster, but Iceland's attitude often disturbed us. I would like to point out that the team kept their heart and soul until the very end, the players fought to make the fans proud of them."
Poland have been drawn in Group E of the Euros alongside Spain, Sweden and Slovakia.
Sousa, though, is under pressure after what some have described as two lethargic performances in their final two warm-up games.
"We have to improve the effectiveness, our game will be modified," he added.
"In the coming days, we will analyse what is still not working out for us. Honestly, I'm not gonna sleep well today.
"I'm going to think about how to build our team's game so that it works well. When I walk, I never look at my feet, I always look ahead. It is similar with this tournament."