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"Burnley had strong pressure in midfield and made it difficult to play. It was more difficult second half because they grew and we had a lot of fatigue, but the end of the second half was very good. We put strong pressure in front and I think we deserved to win.
"It was an important game because it improves our table, four points ahead of Manchester United and Arsenal, which is good."
For Laws it was a first Turf Moor appearance for Burnley since he lined up at right back in a 1-1 draw against Grimsby in May 1983.
Just as was the case four days earlier he was forced into early substitutions, this time one in the first half that saw Christian Kalvenes replaced by David Edgar and then on the hour when Martin Paterson came on for Kevin McDonald.
Laws said after the game: "We picked up a couple of injuries and they are starting to catch us up a little, but there are a lot of positives I can take from this game. The one negative is we could have been tighter with the second goal but apart from that, well done and let's move on.
"I just thought we showed Chelsea too much respect in the first half and let them get on the ball too easily. We set about the second half much better though. We stepped up another ten yards and all of a sudden we were more in the ascendancy.
"That lifted the crowd and gave everyone great belief. The big disappointment is that we were only seven minutes away from achieving a great point. That would have been a great bonus, but I am still taking a lot of positives out of it.
"It was a great goal by Steven Fletcher and I thought we defended really, really well, just on the one instance for the second goal did we give them any space and time and when you do that, that's what you get."
Laws gave a debut to new boy Leon Cort who impressed alongside skipper Clarke Carlisle. "You couldn't ask for a better debut than Leon's," he said. "I thought he was very solid, he defended well and made simple decisions.
"He didn't complicate his game and I am sure as he settles in and gets a few games under his belt we will see what he is all about.
"Overall I think there is some real work in progress. I think everyone can see and recognise that we look a really solid, well organised unit at times. We just need to marry that up now and show the flair we are capable of and if we continue in that same vein, especially against teams in and around us, and with that commitment and drive from the supporters, I really feel confident we can go and win games.
"Getting a point against Chelsea wasn't going to be a decider. It's taking them from sides in and around us and we know exactly where we need to do it now. With our home form and eight games to go here, we feel very confident we can achieve it."
Speaking about the reception he received from the stands, he added: "It was terrific. I couldn't ask for a better reception and a huge thank you to all the supporters for that kind ovation. I was a very proud man and I had a lump in my throat.
It brought back memories and I know the supporters are right behind the players and everyone here. To get that kind of welcome can only inspire people. It certainly did that today and now I hope I can inspire the players on to bigger and better things."