Kenny hails his 'spirited' Lions
Having taken the lead through Liam Trotter's precision finish on three minutes, The Lions then let Burnley back into the game as Ben Mee (19mins) and Charlie Austin (43mins) turned the tables.
Despite two big penalty shouts for handball and a Junior Stanislaus goal ruled out - although replays indicate referee Craig Pawson was spot on with his decision - Millwall refused to buckle and instead fought back superbly with sub Darius Henderson levelling up in injury-time and then nearly nicking it in the dying seconds.
"We showed terrific spirit and we could have won it right at the death," said boss Jackett.
"When you have lost three games on the trot, you need a draw to stop the rot and the players should take confidence from that second half.
If we can eradicate the goals against we are certainly competitive and have players who can score. We have two of the three things needed to win on a regular basis.
We just have to keep working away at it but I felt in the second half it was an excellent performance and we thoroughly deserved the result. We dominated the second half and created a high number of chances."
The gaffer also thought that the officials got it right ruling out Stanislaus' goal adding: "I think it was definitely the right decision.
I couldn't believe the referee was going to give it. Martin Paterson was clearly offside."