Despite a late flourish in the campaign, which saw them lose just three times in their final 10 games, Villa could only finish 15th.
While Villa have fallen to narrow defeats in their last two Premier League games against Chelsea and Liverpool, Lambert believes victory at Arsenal on the opening day shows his side have improved.
"The progress is there for everybody to see," said the Scot.
"That's what I'm pleased about. (If) we play like that for most of the season, we'll have a good season."
Villa were undone by a solitary Daniel Sturridge goal at Villa Park on Saturday and sit in ninth place.
Lambert believes having to play three times in a week has caused his side problems but was happy with his charges' efforts.
"Away to Arsenal, away to Chelsea and home to Liverpool. That's a big turnaround in a week for us," he continued.
"The intensity you have to play at in those three games, especially the two away from home, I've got nothing but praise."
