"We got away with murder at half-time because in the first-half we got killed all over the park," said the Pole.
"We were really lucky to come in at 1-1 but used that to our advantage, defended very well in the second half and came away with a late winner."
Prior to last weekend's victory over Tottenham , the Gunners were 10 points behind their north London rivals, who seemed assured of third place in this season's Premier League.
But their second successive win reduced the deficit to four points, with Spurs facing a difficult match at home to Manchester United on Sunday.
"It's a massive win," said Szczesny, who made a string of fine saves. "It's a little bit harsh on Liverpool because they played really well for 90 minutes but there were games this season when we deserved to win and lost."
There is no doubt that it was a depressing defeat against the run of play and makes Liverpool outsiders now in the race for fourth place.
The lack of a top-quality striker was yet again the most obvious deficiency in Liverpool's side.