Arsenal proved their resilience with the 2-0 win over Liverpool that increased their Premier League lead to five points, said Arsene Wenger.
"It was important to respond to convince people that we can win these big games," said the Gunners manager.
"To win it in a convincing way is even more important."
Arsenal had led the Premier League by two points from Liverpool and Chelsea at the start of Saturday but, with the Blues losing 2-0 at Newcastle in the early kick-off, goals from Santi Cazorla and Aaron Ramsey condemned Liverpool to only their second league defeat of the season.
"Our defensive performance was outstanding," said Wenger.
"We kept Daniel Sturridge, Luis Suarez, Steven Gerrard and then Philippe Coutinho quiet - and for that our defenders deserve a lot of credit."
Arsenal travel to Borussia Dortmund on Wednesday and follow that with a Premier League trip to Manchester United.
Fifth-placed Southampton also visit Emirates Stadium before the end of November.
The 64-year-old Frenchman added: "It was vital to win because had we not won people would say 'Arsenal cannot win the big games at home'. It is done in a convincing way and with good solidarity and focus.
"We have plenty of big games coming up and we have the ability to deal well with them."
Arsenal's lead at the top of the Premier League has been built by a run of eight wins and one draw since the opening day defeat by Aston Villa.
As well as being five points ahead of Liverpool and Chelsea, with a quarter of the season gone they lead Manchester City and Manchester United by six and eight respectively.
"We live in a world where we have to be questioned and the only response we can give is on the football pitch," continued Wenger.
"I am always confident but there is a long way to go. This was an important win for the team, for the club and nobody would dispute we deserved it."
Wenger also revealed that midfielder Jack Wilshere missed the Liverpool game with an inflamed ankle and will need to be checked further before it is known whether he will be available for the trip to Dortmund.