Arsène Wenger praised his Arsenal players for proving they can win key contests against fellow challengers for honours after Liverpool were dismissed 2-0 to hoist the Londoners five points clear at the top of the Premier League.

Arsenal, who have doubts over the availability of both Jack Wilshere and Kieran Gibbs for Wednesday's Champions League group game at Borussia Dortmund, saw his team recover from successive home defeats in cup competitions to move clearer at the summit of the division. Those losses to Borussia and Chelsea had prompted scepticism over the side's staying power – with this came a statement of intent with the return in Germany and then a trip to Manchester United next Sunday.

"We needed to respond today because that Chelsea game, while not as important as this match, was still a disappointment so we had to convince people we can win these big games," said Wenger. "To win it in such a convincing way was even more important. I'm always confident but of course it's a long way to go. Had we not won, people would have said Arsenal cannot win big games at home. But we did it in a convincing way, so it's a vital win at the start of an important week for the team and the club, and no one would dispute we deserved to win.

"We had a good solidarity, a good focus, and I believe we have plenty of other big games coming up and we can do well in them. This is an unpredictable division this year. Who would have said that Chelsea would lose to Newcastle today after the way they played on Tuesday night? That's the Premier League. It'll come down to consistency and, since 1 January 2013, we've had the same group and shown that consistency. Since our massive blip against Aston Villa[a 3-1 home defeat on the opening day], we've been consistent, and 25 from 10 games is a respectable number of points."

Wilshere was absent here with an inflamed ankle, with his fitness to be monitored before the midweek trip to the Ruhr Valley. Gibbs suffered a calf problem late in the match, and will also need to be scanned, but had played his part in a fine team display capped by Aaron Ramsey's wonderful goal. "You cannot single anyone out today," added Wenger. "Our defensive performance was outstanding and kept Sturridge, Suárez, Gerrard, Coutinho and Moses quiet, so our defenders deserve a lot of credit.

"The players know each other better and have improved individually and collectively, and, tactically, we dealt well with what Liverpool offered and stopped them from playing. We are overall defensively a better team these days. But now we go game to game. Dortmund is another big match where we need, absolutely, a result. But this win puts us mentally in better condition. We live in a world where you are constantly questioned, and the only response you can give is on the football pitch. That's what we have done."