Although Tolkien is silent on this point, it is conceivable that Sauron might have regretted the absence of Morgoth following the breaking of Thangorodrim, if Morgoth possessed powers or abilities beyond those which were native to Sauron himself.
And this seems likely, or at least possible, since we know one fact: that Sauron was Morgoth's lieutenant, and therefore that they were not of equal rank and power.
Morgoth covered all the lands with a great darkness during the Elder Days, and, except very briefly, this was a feat which Sauron was never able to match. In the Elder Days that darkness seems to have lasted a great period of time: its exact duration is left vague, but those who remember it (such as Elrond, Galadriel and Treebeard) give the impression that it was not a short-lived event. The implication, therefore, is that Sauron was not as powerful as Morgoth had been, and that he might therefore have benefited from Morgoth's return, had such a thing been possible, perhaps even welcomed it.
A resumption of their former alliance would, at the least, have doubled Sauron's strength - not in terms of the number of his followers or his Army, but in terms of sorcery.
Morgoth might even have possessed superior wisdom. Who can say whether Sauron would have heeded advice even from such a one; but Sauron made a significant tactical error, of a kind which Morgoth avoided, in permitting the greater part of that strength which was native to him in his beginnings from passing into the Ruling Ring, which could thus be taken from him. Who knows whether he would have done so if Morgoth had counselled against it.
From those various perspectives, it might be that, although Sauron failed to realise it, he did suffer from Morgoth's fall; and in that sense he did miss Morgoth, at least to the extent of missing out on the advantages which Morgoth's presence would have offered.
Sauron was himself destroyed and cast into the outer darkness, in the battle on the slopes of Mount Doom in the Second Age, yet he returned after a time. And it isn't entirely clear what prevented Morgoth from doing likewise. So the possibility of his doing so might have existed in Sauron's hopes.