City have already added the Capital One Cup to their trophy cabinet, but their pursuit of an unprecedented quadruple has started to unravel.
Setbacks against Wigan Athletic and Barcelona in the space of four disappointing days have brought an end to City's FA Cup and UEFA Champions League challenges.
A 2-1 defeat at the Nou Camp on Wednesday saw City's European dreams dashed, with Zabaleta seeing red as frustrations boiled over in Catalunya.
Focus has, however, been realigned, with Manuel Pellegrini's side now looking to make the most of their three games in hand in the Premier League title race.
Zabaleta said of the battle to secure domestic success: "We had determination and character in the Camp Nou. It is never easy to come to Barcelona and get the result that we did.
"We should learn about all these things. I am 100 per cent sure if we keep playing like we did there we can win some trophy.
"Hopefully we can keep playing with that intensity.
"We know the only trophy we go for now until the end of the season is the Premier League.
"We know how tough Hull away is (on Saturday) but we have a fantastic team.
"It is just belief and playing with intensity. With this team, playing the way we did on Wednesday, we can beat anybody."
City's hopes of landing a second league title in three years may rest on the fitness of top scorer Sergio Aguero, with the Argentine frontman forced off at half-time against Barcelona as a hamstring problem which kept him out for five games in February flared up again.
Zabaleta said of his fellow countryman and his importance to the cause: "Hopefully it is nothing serious.
"He will have a scan to see if the hamstring is okay. Fingers crossed. We know how important Sergio is for the team and hopefully he can keep fit for the next game."