As for Kawhi...
I can't even... he put on a masterful performance... it just fell shy because the Grizzlies hit a lucky shot at the end... (Marc Gasol shot that with his palm...)
I remember two first round series in which the Spurs lost games on last second shots (Suns '03 / Mavs '14) and the Spurs' seemed to do ok...
What does surprise me is how often the Spurs are on the wrong side of unprecedented situations... and get screwed by the decision-making of the officiating crews or league decisions...
2006 vs. the Mavericks (WCSF): Timmy fouls out of a game by being pushed into Dirk from behind by Dampier - Dirk actually steps on Duncan's foot... but Duncan gets assessed for the foul. Anybody else remember the Mavs getting 50 free-throws in Game 1? Or how about Duncan being deliberately hacked by Dampier on the final putback attempt in Game 7? And still... no whistle.
2008 vs. the Lakers (WCF): The league schedules Game 1 of the WC Finals as an early start even though the Spurs had been held up in New Orleans after beating NOH on the road in Game 7. They didn't arrive in LA until 5 am on May 20th... Game 1 on the 21st at 6:00 pm. The Spurs actually start strong but can't maintain their legs. Kobe and Fisher are allowed to beat up Tony and Manu on their way to a Game 1 win. Then in Game 4 the league assigns recently re-instated Joey Crawford to officiate a Spurs game (to make a point that there was no conflict of interest with his return to the league given the reason for Joey's departure). On the game's most pivotal play, Joey swallows his whistle (Fisher jumps on Brent Barry's back on a last second three point attempt that would've given the Spurs a chance to tie [yes Barry traveled on the play but one had to see that clip in real slow motion to even identify the violation... the foul however was OBVIOUS and should have been called]). Earlier that year NBA Commissioner, David Stern, goes on record saying that his dream Finals would be Lakers vs. Celtics... He got his wish...
2012 vs. the Thunder (WCF): Game 5 and Game 6 were so horrifically officiated I can't even recall how many goal-tending calls Ibaka got away with. Anybody else remember a nullified 3 pointer by Ginobili because they called an off-the ball foul AFTER Ginobili's shot went in... what would've been a go-ahead basket? Then there was Parker who fouled Westbrook on a pivotal layup except Parker never even touched him... a review of the play shows that the whistle was blown before Westbrook even jumped towards the hoop. Those last two games reeked of being rigged.
2013 vs. the Heat (NBA Finals): Everybody will rightfully remember Ray Allen's shot to force OT in Game 6. What they won't remember was Allen traveling on the shot. Or that he stepped out of bounds (right in front of the ref) two possessions prior (which resulted in points for the Heat prior to Kawhi's free-throw miss). Most egregiously of all, no one remembers the fact that Joey Crawford denied the Spurs a chance to catch the Heat flat-flooted after the euphoria of Allen's shot. Ginobili had a streaking Kawhi and would've inbounded the ball behind Rashard Lewis (who would've been behind the play) INSTEAD Joey Crawford stops the game (actually pulls the ball from Manu's hands) to check whether or not Ray's shot was a three or a two... everybody and their momma knew that Allen was behind the 3-point line when he shot that - that part of the shot wasn't even debatable. Popovich is shown on the sidelines furiously yelling something along the lines of "You can't f****** do that!!!" repeatedly at Crawford - who simply smirks back. On the next play, the Heat NOW with a set defense, Chris Bosh fouls Danny Green on a last second attempt - no whistle...
2015 vs. the Clippers (1st round): The Spurs end up as a 6th seed despite having better record than the 4th seeded Blazers. End up with a horrible match up against a streaking Clippers team. It's a fairly officiated series. With one really odd play (again a situational oddity that ends up screwing the Spurs). In the waning moments of Game 7, one of the officials allows the Spurs to set up their play and then "manually" stops the game clock with a device behind his back - giving the Clippers a preview of the play. Rivers makes an adjustment, makes a quick sub - the Spurs aren't allowed to draw up another play - Matt Barnes "reads" the play and intercepts the pass to Kawhi. Setting up the OT.
2016 vs. the Thunder (WCSF): Dion Waiters fouls Ginobili before inbounding the ball in the waning moments of Game 2... the Spurs manage to take possession of the ball on Waiter's badly thrown inbounds (Durant slips), Patty misses in the scramble, but Aldridge is fouled on his putback attempt (no whistle). The whole play should've been rendered moot and Ginobili granted free-throws. Later that series, Adams deliberately trips Danny Green who falls into Durant, Durant gives them the go-ahead points from the free throw line. Next play Spurs miss a shot, and Kawhi tries to purposely foul Westbrook to stop the clock since they are only down 1, but no foul is called - a bewildered Aldridge gets caught flat-footed on defense of the rim - Westbrook And-1 - game over. That whole sequence was crap.
Edit: The reason why I brought all this up was because I saw another such play with less than two minutes left in the recent Game 4 (when the shot-clock failed to reset and Mills rushed his shot). You can't tell me the officials didn't have the authority to stop the game and reset the play. Memphis came back and scored on their end. Do I believe the Spurs will lose the series? No... I do however believe the league is allowing Memphis to be overly physical with the Spurs because they might have a subvert agenda to push for a rematch of the last two NBA Finals - the only team that legitimately stands in the way of that are the Spurs.