Chilwell won the matchwinning penalty converted by Jorginho for the only goal of Saturday's Premier League kickoff.
He said, "We knew coming here it was always going to be a tough match,' he said following the final whistle on Merseyside. 'We've got a lot to work on and improve on but the main thing today was the three points and we got them so we're happy.
"We're a team in transition and we're still trying to work together. We've got new players that have been integrated in and a new ownership so we're still working hard and basically we're just taking every game as it comes."
On the game-changing moment, the 25-year-old was in no doubt that the referee got it right after Abdoulaye Doucare bundled into the back of him as he winded up to fire at goal.
"For sure it was a penalty," he stated. "I was about to shoot and felt the contact, so for me it was a penalty.
"It's going to take a while to get back into the way I was playing before my injury but those are the moments where I want to impact the game, getting the ball in those areas and driving into the box. Thankfully Jorgi put it away as well.
"I've worked hard for a long time for that moment to play in the Premier League again and it just felt amazing to be back on the pitch with the boys. I've had the whole of pre-season plus a few extra weeks where I came in early but it's completely different to this."
Chilwell also welcomed fellow left-back Marc Cucurella for his debut yesterday.
The Spaniard completed his signing from Brighton earlier in the week and will add competition to the defensive ranks, which Chilwell is more than happy about.
"We're at Chelsea so there's going to be a lot of good players," he told Chelsea's website. "Competition for places is going to be fierce and obviously we're going to push each other the same as everyone else in the team.
"They all did really well," he added on the debutants. "They impacted the game really positively so we're very happy to have all of them.
"They're going to help us a lot this season because they're three really good signings."
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