The Gunners were beaten by Aston Villa on the opening day of the Premier League campaign before picking up victories against Fenerbahce and Fulham.
"To lose the first game at home was very tough on everyone," Jenkinson is quoted as saying by Sky Sports News. "I think everyone took it a bit personally and looked at themselves and thought 'that isn't good enough'.
"The last two games we've performed exceptionally and everyone's lifted their game, which was important. We've got to continue to do that if we're going to be successful this year."
Arsenal welcome Fenerbahce back to the Emirates Stadium on Tuesday in the second leg of their Champions League playoff after beating the Turks 3-0 last week.