The Gunners ended the 2014-15 campaign with a successful defence of the FA Cup at Wembley, having secured third place in the table and with it automatic qualification for the Champions League.
Arsene Wenger is expected to strengthen the squad in the summer, with a deal said to be close for veteran Chelsea goalkeeper Petr Cech while Monaco midfielder Geoffrey Kondogbia is another potential target.
Following the Gunners' failure to breakdown Chelsea in their goalless draw at the Emirates Stadium on April 26, which all but ended any outside hopes of a late title surge, Henry claimed his old side needed a "new spine" if they were to challenge again for the championship.
The club's record goalscorer, who led the 'Invincibles' side of 2003-04, has since softened the stance given in his role as a pundit for Sky Sports.
Henry, 37, continues to stress Arsenal must make "a couple of additions" in key areas, but is certain the squad are moving quickly in the right direction.
"It's a difficult task to win the FA Cup back to back, but they have done that," he told Arsenal Player.
"You could see right from the start (against Villa) that Arsenal were going to win the game, and that made it easier for us fans to watch - it was less nerve-racking than the year before.
"So the progress is there, now what we are waiting for is the consistency in the league because that is very important
That is where you can judge a team, in the league.
"Having said that, our generation started by winning the cup and went on to win a double and stayed unbeaten - that is all I can hope for this group to do."
Midfielder Santi Cazorla thrived in the number 10 role during the closing weeks of the campaign.
The diminutive Spaniard believes if Arsenal can retain the focus which was lacking from their early part of last season, then they can be genuine challengers for Chelsea's crown.
"We would obviously like to prepare ourselves for possibly for a better campaign in the Champions League and the Premier League," he said on the club's official website.
"One of the things the team has to focus on more is mental toughness and consistency.
"There have been games that we have not won that we should have, so we have to be more consistent to get to the next level."
Arsenal head to the Far East for the Barclays Asia Trophy Singapore in mid-July, and will open the domestic campaign against Chelsea in the FA Community Shield at Wembley on August 2.
The Gunners host West Ham in their opening Premier League fixture.
Source : PA