Yakubu took his haul for the season to 15, with his second treble of the campaign - the first came in December against Fulham.
David Moyes said: "I am really pleased with the performance and the goals we scored. We could have had more, we hit the woodwork twice and played some excellent stuff.
"Overall, to score six in European competition is terrific. We didn't take any chances with the team, we put out a strong side because we have been knocked out of too many cup competitions in the past. We made sure we were strong from the start.
"It's Fiorentina next, and that will be a really good tie. I saw them last week when they won the first leg in Oslo against Rosenborg and they are an excellent outfit.
"It is a game we will all look forward to, but we know it will be tough because they are doing very well in the Italian League at the moment.
"You only have to see how good the Italian sides have played over the years, we have witnessed it in this city. They will be tough to break down, we saw Inter Milan doing that this week.
"They have got some good players up front, Adrian Mutu is scoring a lot of goals for them so we know how tough it will be."
He added: "Yakubu did so well. That is not a bad first game back at Goodison Park after his spell with the African Nations Cup.
"That's what he does, scores goals. We have always known he has got that in him. His second when he sent two defenders the wrong way was terrific.
"His first was crucial. They came at us for half an hour and got at us, which you would expect with them 2-0 down from the first leg. So we needed to get the first, that was vital and Yak produced a great effort."
Yakubu cost a club record £11.25million last summer, and Moyes said: "I knew Yak had a good record of goals with both his previous two clubs in the Premier League.
"I felt if he could add that same amount of goals to what we already had here it would improve us. I was only thinking of the goals, we had the work ethos.
"I was pleased too with Andy Johnson. He works so hard and sometimes chances bobble away from him. But he got one early and hit a pearler at the death, so for our strikers to get five goals is very good."