A second-half collapse saw the 'Cottagers' slip from 1-1 to 5-1 down as the 'Gunners' ran riot after the interval.
The defeat leaves the newly-promoted side struggling at the wrong end of the table, having conceded 21 goals in their eight games of the season to date.
Speaking after the final whistle, Jokanovic criticised his side's defending, urging them to improve quickly.
"We played the first 45 minutes well, created chances and gave them questions. But in the second half they scored very easy goals. We opened all the doors," he lamented.
"At the moment we're showing so many weaknesses for the level we are at, defensively. We need to improve quickly on this.
"I believe my team tried. After they scored a second, I tried to find some way to equalise the game. We finished the game with 21 shots, and the other team nine. But they showed the quality, the pace, the strength too."
However, the Serbian rejected suggestions his side should adopt a more cautious approach to playing the ball out.
"We must trust in ourselves, we must keep working," he insisted. " At the moment we haven't showed Premier League level, it's true. It's not an easy competition. We must be brave, be strong, push forward, and be ready for the next challenge.
"We tried to win the game. I trust that if I try to win the game, one day I will win the game. If you believe the solution is to sit in your box, I don't believe in that way. Anyway, when they arrive in the box you find so many problems.
"Today we tried, but we didn't play well enough. We showed some positive signs but it's not easy for me to now explain so much about those positive things."