The Eagles trailed after 45 minutes against the Gunners, but flew out for the second half and were able to pull level through Townsend on 49 minutes.
Despite the improved intensity and a quick equaliser, Palace were unable to prevent a quickfire Alexis Sanchez double, which would eventually secure the three points for Arsenal.
"I think everyone was disappointed at half time about the performance, it wasn’t good enough," said Townsend. "We sat off and gave them too much space, too much time on the ball, and a quality side like Arsenal will punish you and they did in the first half.
"At half time the manager told us not to be afraid of them and to take the game to Arsenal and I think we did that in the second half. We gave a good account of ourselves but unfortunately we came up a little bit short."
The Eagles' first goal came through Townsend guiding a Wilfried Zaha cross beyond Cech after good play by the Ivorian on the wing - and the number 10 was quick to recognise the assist, racing over to celebrate with him in front of the Holmesdale.
"Of course [I ran to Wilf]. He did all the hard work and I just had to guide it into the goal," said Andros. "It was a huge relief for myself, I’ve been frustrated that I’ve not been able to chip in this season and take the burden off Wilf a little bit, but that weight has gone now and hopefully I can relax a bit more and chip in with goals and assists."
Townsend also looked ahead to the Manchester City game and discussed remaining fresh over the festive period. Watch the full interview for free HERE.