The Hoops left-back wore a T-shirt with a message in memory of former Honduras team-mate and ex-Rangers midfielder Arnold Peralta, who was shot dead in his homeland on Thursday.
Izaguirre described Peralta as a “brother” and, despite his anguish, he helped Celtic go four points clear of Aberdeen at the top of the Ladbrokes Premiership, with a game in hand.
Striker Nadir Ciftci helped himself to a double, with Dedryck Boyata scoring a header.
Deila said: “I talked with him and he was ready. I trust my players and he did a good job. It was hard for him, but he wanted to play and I am very pleased with the way he got through that game, if you take into consideration the circumstances.
“He made that choice himself and it was important that I didn’t have it over his head.”
The Norwegian boss was also pleased with the performance of keeper Craig Gordon and Ciftci, who was playing again due to an injury to top scorer Leigh Griffiths.
Gordon had been at fault for Fenerbahce’s goal in the 1-1 draw in Istanbul on Thursday night which had concluded a doomed Europa League Group A campaign.
However, he denied point-blank shots from Michael O’Halloran in the first minute and Murray Davidson later in the first half, while Ciftci showed why Celtic signed him from Dundee United.
Deila said: “I am very happy today with Craig Gordon. He was very important in the first-half, but also the whole defence, who dealt with a lot of crosses and pressure.
“We have spoken about getting a settled defence, but now you see consistency, improvement and you see that Craig feels more safe and that makes him the goalkeeper he is and today he showed his class.
“I am so happy for Nadir. He now has had two games in a row and we know he can do things.
“Today, he was strong and scored two goals and it makes it better for everybody that we don’t have to rely on Leigh all the time.”