The 25-year-old England midfielder, whom Mourinho courted during his time as Manchester United manager, was sacrificed early for contract rebel Christian Eriksen with the Greek side taking a 2-0 lead after just 20 minutes.
Tottenham rallied back as Dele Alli halved the deficit just before the break, and an improved second half performance saw the North London side qualify for the knockout stages of the competition with two goals from Harry Kane and one by Serge Aurier.
Despite Mourinho’s changes getting Tottenham back into the match, the Portuguese manager admitted the most difficult moment of the night was having to hook Dier off so early.
"The most difficult moment of the game was not when they scored the first two goals, it was when I made the change in the first half," Mourinho said.
"It hurt the player but also myself. It's not easy for him or me. It's important that the player understands, and I was lucky my choice was a very intelligent boy who has very good understanding of what the team is, because I did it for the team. It was not about his performance, but what the team needs.
"We are losing 2-0, in a very difficult situation in that moment, and I felt that one positional midfield player was enough. I thought I needed a second creative player who could play with Alli in what I call an open triangle, and not with a closed triangle with two deeper midfielders. I apologise to Eric, but he knows I did it for the team and not to hurt him. I think the fans understood too."
Tottenham are back in action against Bournemouth in the Premier League on Saturday as Mourinho looks to make it three wins from three.
