Manager Sam Allardyce said: "It was great Nicolas was in the vicinity of James because his pace meant no-one was going to catch him.
"You have to admire him not just for his scoring record but for his all-round play.
"When I see him chasing an opposing defender down, running 30 yards to take the ball off him and creating another attack I know I am winning."
Redknapp revealed he tried to sign Anelka in the summer.
"He is a quality player - a bit special," said the Portsmouth boss. "He has a terrific ability and his confidence is high. Sam has bought a very good player."
Despite their first defeat in seven games, Redknapp took positives from the performance.
He said: "We passed the ball around for first 20 minutes and looked fantastic.
"But we knew it was going to be hard. They keep coming and make it difficult for you.
"Eventually Bolton got the breaks but they have a lot of ability as well.
"Their keeper made a couple of great saves. You would have fancied Andy Cole to have scored nine times out of 10 when he had a chance.
"But it was a great finish at the end and it was good to see him play a full 90 minutes.
"You always want to win but we have had some great results recently and are doing well.
"It is important we remain confident in our own ability."