The defender suffered the injury in stoppage time to compound a miserable afternoon for Tottenham at the Emirates Stadium as they lost 3-0 to their North London rivals.
Bassong admits it was the low point of his Spurs career to date and has now ruled himself out of action for around a month.
"It's not good news. It's a hamstring. I'll be out maybe four or five weeks. It just feels like my muscle is gone," he said in the Daily Mirror.
"It was really not a good day for me or the club or the fans. It was the worst day of the season."
There had been plenty of discussion before Saturday's derby about whether Tottenham had narrowed the gap on Arsenal.
Spurs had already lost to Manchester United and Chelsea this season and did not look like getting a point against the Gunners from the moment they conceded twice in a minute just before half-time.
ImprovementManager Harry Redknapp believes his men should be pushing for a top-four finish but Bassong feels a lot of improvement is needed.
He explained: "When you see that game, we can't stop at this level. If we stop working, we will be disappointed again and again. So to be in the top four we need more, much more.
"If we want to be in the top four, we have to win against these teams - Arsenal, Manchester United, Chelsea, Liverpool, Manchester City - and if not it's going to be difficult.
"This game just proved that we need to keep working and really work every day. We lost the game in one minute. In one minute we messed up the whole game.
"We've got big quality in the squad and we can still look to take that fourth position in the table but we need to work hard, stay focused and we need to improve."