You won't like this, but the correct decision was to award a goal. I will try and explain simply why...
The ball was initially played to the winger who was onside but the CF was offside.
Because the ball went to the onside player (winger) and the striker didn't recieve the ball or interfere with an opponent who could get the ball (how could he if he is in the middle of the pitch) then the correct decision is to play on. Assuming when the winger crosses to the stricker (2nd phase) the stricker is now onside, then the goal has got to stand.Years ago (more than 10) the offside law changed from the old
"if someone is offside, give a free-kick" to the newer version
"give the free-kick if an offside player interferes with play or an opponent". You get pricks like Andy Gray and Alan Hansen who say rubbish like "why do they keep changing it?" (they don't, and haven't changed it for about 10 years) and "why don't they go back to the old method?" (because the "new" method is fairer and you get more goals as a result - therefore matches are more entertaining).
I guess the reason why the ref didn't have his book to show you why, is because the latest one is 140 pages long and would take a bag on its own. If you want to understand more about the offside law, you can download a pdf version at
http://www.thefa.com/TheFA/RulesandRegulations/~/media/Files/PDF/Get%20into%20Football/Referees/lawsofthegameen_0910.ashx/lawsofthegameen_0910.pdf and look at pages 31, and 100-108.
Now , cue the jokes about "interfering with an opponent"!