Compressed sensing is not a particularly efficient type of compression, see e.g. Goyal, Fletcher, Rangan 2008 DOI: 10.1109/MSP.2007.915001. That being said, compressed sensing per se is not even compression in the information-theoretical sense - it is a dimensionality reduction (reduce large vectors of continuous values to smaller vectors of continuous values). This does not take into account that the measurements must be discretised (quantised) in order to be able to talk about compression. Doing this (discretisation), you have a trade-off for a given bit-rate between few measurements at high resolution vs many measurements at low resolution which can affect the reconstruction quality a lot. This trade-off is not particularly well characterised in the literature (but see e.g. Laska & Baraniuk 2011 DOI: 10.1109/TSP.2012.2194710) and even then, reconstruction quality will depend a lot on the reconstruction algorithm and how it possibly takes the discretisation into account.
In other words, you might be able to get better results by trying more measurements at a coarser quantisation or fewer measurements at a finer quantisation.
Compressed sensing (with quantisation implied) has also been proposed as a "cheap" digital compression technique for low-energy wireless sensors (e.g. Liu, Zhang, Xu, Fan, Fu 2013 DOI: 10.1016/j.bspc.2014.02.010). That is, you first sample "normally" in the Nyquist sense and then apply the measurement matrix digitally. When considering compressed sensing like this (which I am guessing is what you did), the argument is that applying this compression (depending on how dense the measurement matrix is and whether it can be applied via "fast" operators such as FFT) is cheaper than traditional compression and the "hard work" of reconstruction in the case of compressed sensing is off-loaded to the receiver side.
Particularly if you can use a Fourier-like transform (DFT, DCT, DST...) as your sparsifying dictionary, you can get away with sampling at lower rate in the time domain in a simple way where you take fewer samples than the Nyquist rate dictates at discrete (preferably random) time points.
I general, I find that compressed sensing mostly makes sense in applications where the possibly analog "compression" represented by the compressed sensing measurement matrix enables sensing that was not otherwise possible - for example by enabling cheaper sensors or lowering the sampling rate or reducing the total sampling time from an unrealistic to a feasible sampling level. First sampling a signal traditionally according to Nyquist and then applying compressed sensing in the digital domain does not make much sense - with low-energy wireless sensors as a possible exception in some cases.