To me, "banana" says "stressed yeast". That usually means high temperature fermentation or underpitching. If the ambient was 60 degrees, you were probably ok, but it's important to monitor the temperature of the beer, not the ambient temperature. A "stick on" thermometer can easily fix that.
Some yeast strains taste fruity if fermented above 70 degrees or so, so it's possible that your temperatures creeped up above 70, but not likely unless you pitched the yeast before the wort got down to 65 degrees or so after brewing.
Underpitching is more common with liquid yeast, so if you used a liquid strain, that could be the problem if you didn't make a starter. Dry yeast tend to have enough yeast cells in a package, so it's not needed.
Some yeast strains, like hefeweizen yeast, are notorious for being banana-y but if you didn't use a "fruity" yeast strain, then I doubt that would be an issue at all.