Barca head into the second leg of a UEFA Champions League last-16 tie holding a commanding 2-0 lead.
Victory at the Etihad Stadium has put them in pole position to reach the quarter-finals, but aware of the need to complete a professional job on home soil.
City are expected to try and get on the front foot in Catalunya, as they seek a route back into the contest, but Alba claims Barca will be doing all they can to prevent the encounter from opening up.
The Spain international told Sky Sports: "The score in Manchester was excellent but the game is not decided.
"City are a big club and are dangerous in attack. We are prepared for the battle.
"A match with many goals would not be good for Barcelona. We need to control the situation.
"The first match was a good test and now we need to close things out and focus again on La Liga.
"At home we are always expected to put in a lot of effort. Our objective is to win and prove our level."
On the threat City will pose to Alba and his defensive colleagues, the attacking full-back expects former Atletico Madrid frontman Sergio Aguero to be a handful - but one Barca can manage.
He added: "Kun Aguero is very important for City, but all of their players are dangerous.
"I have played against the Argentinian in La Liga and we stopped him them. On Wednesday, if he plays, that will be our objective again."