The victory puts them three points clear at the top of Group F and a win over the Moscow side at Stamford Bridge in a fortnight will guarantee the Blues a first-place finish.
"I think that we played a good game," said Ancelotti. "It was not an easy game because Spartak, above all in the second half, played well.
"But we established good control in that first half, scoring two goals, and then controlled it defensively in the second. We played well at the back, above all Petr Cech, who made some fantastic saves."
"It was an important moment for Yury, coming back to play for Chelsea in Russia. He scored a fantastic goal and will be very happy.
"He was very good. He played very well and doesn't have a problem playing either left-back or on the left of midfield.
"He scored a very important goal and opened up the game. After that, it was easier for us to win the match.
"Anelka showed his qualities and ability to play in front. He's comfortable playing up there when there's no Didier Drogba. He's a fantastic player and can play in all the positions across that front line.
"I think Spartak are a very good team with different skills. They used all the pitch to attack in the second half, with good players at the back pushing the play forward. They have the same possibility to arrive in the last 16.
"We are not in the last 16 yet. We have to play three games and must do our best in those matches.
"We have to stay focused about the next game. We want to finish in first place. That's our aim.
"We will have the possibility to do this, but it doesn't mean we have to rest the other players. The Champions League is an important competition every time you play. For all the games."
Spartak boss Valery Karpin bemoaned his team's poor first-half performance and insisted they would hope to gain some points from the return clash in a fortnight.
"We had two different halves," said Karpin. "I spoke to the players in the dressing room and realised my team were a bit scared of Chelsea in the first half.
"We conceded two goals in the first period and only had the fighting spirit after half-time. It was not enough.
"We will focus on the re-match in London and produce good football there and get some points."