Michael Laudrup's side snatched a late draw against the Blues on Saturday, with Pablo Hernandez striking to cancel out Victor Moses' earlier effort.
The 19-year-old Welshman saw a great resolve in his team-mates over the course of the game and also felt Roberto Di Matteo’s side met their match in the Swans' controlled pressing and passing setup.
"They are a top, top team, but there didn’t look a class difference out there for most of the game. I thought we matched them throughout the 90 minutes," Davies told Swansea’s official website.
"We are a fit squad, which helps against teams like Chelsea when you have to chase the game.
"We showed great character to come back from a goal down. We never stopped believing in ourselves and got what we deserved out of it in the end.
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"We all worked hard for each other out there – and that’s what we do in every game. We always give 100 per cent. Even with the boys that are subbed during the game, it’s normally because they are shattered after the work they have put in."
The Wales international feels the team can also take many positives from their performances against the better teams in the division after narrowly losing to Manchester City, beating Liverpool in the Capital One Cup and matching a free-flowing Chelsea stride-for-stride at the weekend.
"We performed well in all three games this week," Davies added. "They were all tough; all big tests for us; but I thought we came through them very well.
"It will give us great confidence going forward. We know that if we can get results against the better teams in the league then we should, if we keep working hard, pick up the wins we want against the teams fighting with us in the bottom half of the table."
Davies has been tasked with stopping Samir Nasri and Victor Moses over the last week and has come out of these encounters with a new-found confidence and glowing reviews from his manager.
"The gaffer just tells me to keep doing what I’m doing," he added.
"He says that if he didn’t think I was ready then he wouldn’t put me in the team. It gives your confidence a boost when he puts you in the team to play the likes of Chelsea and Man City.
"It is a great experience to come up against players like that, but I’ve just got a job to do against them."