The Blues leapfrogged reigning champions Manchester City in the top-flight standings by beating the Eagles 2-0 at Stamford Bridge, with Tammy Abraham and Christian Pulisic grabbing the goals.
Abraham's tidy finish opened the scoring in the 52nd minute, before Pulisic made sure of all three points with a powerful header 10 minutes from time.
Chelsea are now only five points behind league leaders Liverpool, who host City at Anfield on Sunday afternoon.
Lampard is not thinking about a tilt at the Premier League crown yet though, with it his belief that there is still a gap in quality between his side and last season's top two.
"We’re just happy with what we’re doing," the 42-year-old told BT Sport post-match. "We’re working hard. It’s great to go into the international break off the back of that.
"At the start of the weekend, we can sit back a little bit now and watch the other games, and we respect where Liverpool and Manchester City are, and that was the gap to try and bridge in some way going into this season.
"At the minute we’re staying close and we’re on good form. I was a little bit frustrated [at half-time]. We allowed the tempo to drop through the half.
"We started pretty well, if we get the early goal it feels a different game but, as the game went on, it became a bit broken, we were a bit slow with throw-ins, and re-taking free kicks, forward passes and I just felt if we increased the tempo the game was there to win. The players went out and did that."
Abraham, Mason Mount, Fikayo Tomori and Reece James all put in strong shifts against Palace, continuing to show a maturity belying their age.
Lampard has been rewarded for his faith in Chelsea's academy stars at the start of his managerial reign, and claims he knew they were ready for a step up to the senior fold having "watched them from afar".
"I did believe in the younger players," he added. "I’ve watched them from afar. We know the academy well. Not just myself, Jody, Joe, Chris Jones.
"We do feel the club and we know them so that gave us a little bit of a headstart on that point but you never know with young players until you put them in and when you put them in in a bit of a group, even more so. If you’ve got two, three, four in there they really have to step up quickly at this level or it won’t last.
"They’ve clearly shown they have the ability, the mindset, the desire to play for Chelsea. They’re surrounded by some fantastic experienced players.
"I mentioned Azpi, and his attitude week-in-week-out and Willian’s work-rate today, people want to think of him as a winger and judge solely on that but I massively judge him on what he does off the ball and his constant running.
"Kante playing in there, Kovacic, Jorginho’s not there today, I could go on and on. The balance we’ve got feels good, which is obviously helping the young boys."
After the international break, Chelsea will resume their Premier League campaign with a huge showdown against City at the Etihad Stadium on November 23.