Henry, who won two titles while at Arsenal, hopes that the Gunners were celebrating qualifying for Europe's elite competition at the expense of north London rivals Tottenham.
"Putting Tottenham out of the top four, and I really do hope that's what they were celebrating about, that's the only thing you can celebrate," said the 35-year-old New York Red Bulls striker to Sky Sports.
"If you're an Arsenal man through and through that's like winning something.
"I said it when we did to them in 2006. It wasn't the fact that we qualified for the Champions League, it was because we kicked them out of it and we went in.
"Yes, they finished in the top four but there is only one champion - Man United. I'm a competitor so that's the only thing I will remember from the season - Man United won the league. You're going to have to do better than what United did this year.
"Chelsea I'm sure are thinking about the same thing right now, or Man City. Tottenham are going to think, 'how can we come back into the top four?' All the teams are going to be thinking, 'how can we win this title?'"