The Cowboys took the lead three times, including opening up a seven-point gap midway through the fourth quarter, in an exciting match that saw momentum swing from side to side.
Witten, who had 121 receiving yards and a touchdown to his name, made no effort to hide his disappointment at the result, but urged his side to show similarly impressive offensive performances in their remaining games.
"So you leave this game and obviously you are crushed and disappointed. Offensively, this needs to be the standard by which we play," Witten told The AP.
The Cowboys, who are now 2-3 for the season, set a franchise record for number of points scored while still losing in yesterday's match.