And if Arsene Wenger's side beat the Trotters when they meet again at the Emirates Stadium on Wednesday, they will go top of the table.
Fabregas told Sky Sports 1: "Maybe scoring more goals is just luck because when I was younger I had so many opportunities and they weren't going in.
"But this year they are and it's important that they keep coming. I have been training for a few years in front of goal and I feel stronger and that helps in the last yards."
The Spaniard was also proud of the effort his side put in to claim the three points.
He said: "It is always difficult to come to Bolton and we are proud to win. They are a difficult team to play against and we respect every team, it is important to win again on Wednesday for the title race."
Arsenal boss Arsene Wenger praised the maturity of his young side as they survived a sustained period of pressure from their hosts when 1-0 up, before going on to get the crucial second.
"That was a big win and they had full commitment with a new manager, they played a lot of long balls and the pitch wasn't easy to play on," he told Sky Sports.
"We got through a patch where they could have equalised and then got the second goal.
"We have matured, some players have much more personality on the pitch and that helps us get results."
Wenger was also full of praise for his captain, saying: "When I speak about players with more personality on the pitch, I have to talk about him. He has an authority, he scored again and was very influential."
The Frenchman is expecting another tough game on Wednesday in the rearranged clash at the Emirates.
"It is unusual to play the same side twice in three days and they put a lot of effort in today and we will face the same problems on Wednesday," he added.
Bolton boss Coyle felt his side were unfortunate not to get anything out of the game.
"That was very harsh on us, with what we offered to the game on another day we could have had a positive result. We had numerous chances and the ball didn't break for us on occasions," he said.
"The second half belonged to us and we created plenty of opportunities, we pushed forward to get that equaliser and got caught for their second, although I thought Eduardo was offside when they crossed it and we paid a heavy price for that.
"If we play at that level, we will pick up points in this league and we can make a game of it on Wednesday."
Coyle also joined Wenger in praising Fabregas' display: "Cesc could play for anybody in world football, he is an outstanding player," said the Scot.
"If you give him time and space he will harm you, but I thought our lads offered plenty of effort."
And Coyle is confident he can get his side up for Wednesday's rematch with the Gunners.
"It's not an ideal situation but that's when it has to be played. The guys down the bottom of the table will be delighted to see us play them again, but we feel we can go there and it's a game we are looking forward to.
"If we put in a good performance, we can get something."