Arsenal's wait for Premier League glory is approaching its 11th year after the club finished fourth last season, five points adrift of champions Manchester City.
During that 2013-14 campaign, which saw them win the FA Cup, Arsenal lost seven games, with four of those coming against the so-called 'elite' clubs.
The London club were humbled by Manchester City (6-3), Liverpool (5-0) and Chelsea (6-0), while they lost 1-0 to 2012-13 champions Manchester United.
Arsenal were also beaten 3-0 by their rivals for UEFA Champions League qualification Everton, who finished fifth.
Speaking to reporters after Saturday's 1-0 pre-season defeat to the New York Red Bulls, Wenger was aware his side had to perform better in order to win their first league title since 2003-04.
"That we were not far [away], it was very tight. We wanted to add that little bit of quality which we missed in the end," the Frenchman said.
"It depends on one or two games at the end of the day. There's 38 games, we finished with 79 points, the winner of the championship had 86 so it was very tight.
"Hopefully we can get that little bit more quality in the decisive games. We were more consistent than everybody else against the lower teams, we performed less well against the top-level teams so that's what we have to gain."
Arsenal - missing forwards Alexis Sanchez, Olivier Giroud and Lukas Podolski - were unfortunate to leave New York empty-handed after Bradley Wright-Phillips made the breakthrough on Saturday.
Jack Wilshere was denied on two occasions just minutes before the half-time interval, while Abou Diaby found the back of the net only to be flagged for offside.
However, Wenger was just happy to emerge from the match with no injury concerns.
"It was not ideal but we got away without any injuries," the Frenchman said.
"The bad thing is that we couldn't score and we lost the game, the good thing is that we gained something out of it physically and we have no injuries."
Arsenal will open their Premier League campaign at home to Crystal Palace on August 16.
