Fabregas played for just over an hour and scored a penalty as the Ukrainians were brushed aside at the Emirates Stadium.
"I wanted to have 60-70 minutes and at 3-0 it was time to come off," the Spaniard told Sky Sports 2.
"I didn't feel anything, it felt great. We thought it was better to start the game because mentally you are more ready and you warm up better. It felt fine."
Arsene Wenger was also pleased with his captain's progress and said: "We were a bit cautious and apprehensive in the decision but the fact he got 60 minutes without injury is very good."
Arsenal have now scored 14 goals in winning their first three games in Group H, but Wenger added: "Let's not deduce too much, we have shown good quality but it is just the start, let's continue to improve.
"I am cautious because as soon as you lose urgency your level drops dramatically. The team has good potential, and they have shown that again tonight."
On Fabregas' midfield colleague Jack Wilshere, who was also among the goals, Wenger said: "His maturity is miles ahead of his age, and that is a sign of his talent.
"I am happy Jack got a goal because he ran after it for some time."
Wilshere added: "I've had a lot of games now and scored a couple, hopefully I can get a few more games now."
On his side's goal glut - which also saw Alexandre Song, Samir Nasri and Marouane Chamakh find the net - the teenager said: "I think it shows we're ready for the competition, even in the Premier League we're scoring goals.
"We started off sharp, they couldn't handle us and we got the goals."