The 24-year-old Belgium international said the Blues had a “bit of luck” but was pleased to celebrate after Wednesday’s game at Stamford Bridge saw Chelsea secure a 2-1 win over Everton.
He said: “We had a bit of luck and showed a lot of spirit until the end.
“It was great to win that fight. Congrats to everyone. We move on.”
Antonio Rudiger’s first-half goal gave Premier League champions Chelsea the lead against an Everton side led by caretaker manager David Unsworth.
Brazilian attacker Willian doubled Chelsea’s advantage in injury time, though the Toffees grabbed a consolation before the full-time whistle.
Antonio Conte heaped praise on his young players, who coped with a fighting Everton display during the second-half.
After the game, the Italian manager said he saw a lot of “positive things” from the players and believes Batshuayi is ready to start games regularly for Chelsea.
The striker was rewarded for his two goals in the comeback win over Watford on Saturday with a start at Stamford Bridge against Everton.
Other players to impress Conte on Wednesday included 17-year-old Ethan Ampadu, who got his second outing for the Blues, and Charly Musonda and Kenedy.
Chelsea now turn their attention back to the Premier League as they prepare to visit Bournemouth, who are chasing a third straight win.