It really depends on your target audience. Remember that more people can reach a website than an app. While mobile phones have browsers, the computers can't necessarily access a mobile app. However, depending on the type of system you're building you may not care if someone can access it from a browser. There are plenty of examples where mobile only makes perfect sense.
Back to your initial question, the web has not lost its impact and i think will only gain more importance as time goes on. What I think you'll start to see more of is the appification of the web as evidenced by the growth of hybrid apps, the new instant apps for Android and other platforms that aim to create an app from the web. Apps were the new hotness that everyone loved and the band wagon everyone wanted to ride on, however, it's become obvious that maintaining several apps for several platforms can be tiresome and costly, whereas a website designed to work like an app can perform most of the same functions and exist on most platforms everywhere.
Apps still make sense, but I think the massive drive for them is slowing down and you're going to start to see web come back. Maybe not in the exact same form as it was several years ago, but perhaps as something a little more evolved that can serve the different platforms more natively.