I see both sides of this question but I would have kicked the field goal as well. The advantage of the field goal is that if it is made, we and now within a field goal of the win and we don't need to score any TDs which are clearly harder to do that getting field goals. This game showed that clearly. The other advantage is that assuming you make the kick, you get to kick off and have a chance, albeit a small one, of getting the ball back with an onsides kick. This allows the offense to control the remainder of the game and you don't even have to worry about whether or not you are able to prevent the opponent from running out the clock with a first down or two, no matter the time left or time outs, etc.
If you miss the kick, you get to go on defense at that spot and of the field without worrying about a kick off return against you or the time running off for that play or a bad kick out of bounds or something of that sort. We did have to rely on Brown to make a TD saving kick off return tackle already in the game as well.
Yes, the 4th down attempt would look great if it worked and we went on down and scored the TD and used up the clock in the process but that didn't happen and we were not exactly controlling anything offensively such as the line of scrimmage battle, etc. Our QB was getting sacked and hit repeatedly throughout the game. The chances of scoring a TD on a long drive, as we did to end the game, were very low (less than 10%) surely. You might have an 80% chance of Brown making two field goals kicks and a 10% chance of recovering the onside kick. If not, you still get to play defense with about the same time and time outs etc.
