Declan Rice says Arsenal are ready for more grinding wins as he hailed the 1-0 success at Liverpool on Sunday as the performance of champions. The midfielder set up Kai Havertz for the only goal on 16 minutes but his defensive work was arguably more impressive; his physicality and reading of the game.

Liverpool were unhappy at the non-award of a penalty for a Jürrien Timber shirt-pull on Alexander Isak in the 21st minute and it was a day when the Kop fumed about Arsenal’s streetwise tactics, especially how they won free-kicks – albeit their own players were also guilty of going down too easily at times. The Arsenal goalkeeper, David Raya, was booked for time-wasting in the 92nd minute as his team closed out the victory.

Arsenal won 1-0 at Nottingham Forest in their previous Premier League away match – after which they were criticised for their lack of creativity. This time, the barbs centred on their gamesmanship because they were a threat on the counterattack. They are not about to trouble anybody connected to the club.

“No game is plain sailing; it is always going to be tough,” Rice said. “Looking back at that Forest game, it wasn’t the best performance but we ground it out, we won and there’s going to be more of that this season. But results like this one [at Liverpool] just make it that extra bit special so we are delighted.”

It was Arsenal’s first league victory at Anfield since 2012 and they have won at four grounds where they did not win when securing the title last season, the others being Villa Park, the Stadium of Light and the City Ground. “Any team who has won at Anfield in the past has never had it easy,” Rice said. “We had to dig in and give it everything because they throw so many attacks at you. We had to be resilient and strong. It was a great win.”

Rice was asked whether it was a match in which Arsenal had played like champions. “For sure,” he replied. “It’s just drilled into us. What the manager [Mikel Arteta] has built at this club and the togetherness of the lads – you don’t get that performance without the lads being all together.

“The way the manager has everything under control, the way everyone works towards everything he wants is not like anything I’ve ever seen before. So credit to us for what we have been doing for the last few years. Now it’s a massive thing to deliver again this year.”

Dominik Szoboszlai said Liverpool’s defeat demonstrated there were only fine margins between Andoni Iraola’s side and the Premier League champions.

Liverpool failed to register a shot on target in a Premier League home game for the first time since records began in 2003-04, according to Opta, as Arsenal moved three points clear at the summit. Szoboszlai believes the contest turned on the Isak shirt-pull incident and that there was little between the teams.

“We are just one penalty less and that’s a big difference,” said the midfielder. “You know Anfield, you know our quality. I know they are a great team but it wouldn’t be easy for them [to have come back from a successful penalty].”

Iraola claimed he would tell Liverpool players to go down in the box but Szoboszlai said that was not their style.

“I don’t think in this moment you can think: ‘Oh, let me wait for someone touching me and I’ll fall down,’” he said. “No, Alex is focusing on the ball and he wants to head the ball in the net … It’s a penalty. I don’t know what they expect from us, to dive or something? I don’t think we are the type of team or players to do that but from now on we might need to do it. If Alex falls down it’s a clear penalty. Timber doesn’t really care about the ball and maybe if he doesn’t pull Alex’s shirt Alex can head it in the goal.”