While people may (and will) argue as to whether there was a single "smoking gun" that made it obvious it was Roth, Michael must have had suspicions about Roth already. A few years back Michael had Roth's protege, Moe Green, murdered and now Michael was moving in on Roth's businesses in Las Vegas and Cuba. So Michael must have assumed that there would be a response at some point to this.

In addition Michael doesn't want to tip his hand to Roth because he still doesn't know who he can trust in his Family. Someone had (inadvertently or otherwise) to give Roth's gunmen access to Michael's estate, information about Michael's whereabouts, etc.

So he goes and does his "dutiful son" routine to Roth, who appears to eat it up. Notice that Roth does not appear to be saddened, frustrated or angry about the attempt on Michael's life.

Then Michael appears in NY, unbeknownst to Pentangeli, and lets his true feelings show. Pentangeli is frightened and angry but most importantly Michael gets the accurate sense that Pentangeli is too loyal to have made an attempt on his boss' life. Pentangeli is also not as skilled as hiding his true feelings as Roth is. If it wasn't Pentangeli then it was likely Roth.

If Frankie was hellbent on disobeying Michael he probably just would have started an open war with the Rosato Brothers, rather than take the much riskier step of killing a Family head.

While Roth obviously would have preferred that his hitters got Michael in Lake Tahoe, he also would have liked the possibility of an alive and enraged Michael launching a war against the Pentangeli faction of the Corleone Family.

Micahel gets confirmation of all this when he asks Roth "Who killed Pentangeli... Who gave the order? I know I didn't.."