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Both the Reds and the Blues were left outraged by Tierney and on-field referee Sam Barrott during a heated encounter at Anfield.
Liverpool were left furious on ten minutes when James Tarkowski lunged into a challenge on Alexis Mac Allister.
While the ball was played by the defender, the follow-through saw Tarkowski catch the midfielder with his studs just below his knee.
Barrott immediately gave a yellow card for the challenge, but it was expected that VAR, Tierney, would overturn the decision.
Instead, after a short check, play was allowed to continue with Liverpool fans and neutrals bemused.
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Tarkowski has since apologised to Mac Allister, who accepted the gesture.
In the second half, though, it was the Blues who were left reeling with the officials as they felt Luis Diaz was offside during the build-up to what turned out to be a winner from Diogo Jota.
Everton captain James Tarkowski fouls Liverpool midfielder Alexis Mac Allister.
I think the player is behind Tarkowski, interfering with him clearing it [the ball].
"It's a clear offside, and I think it's a very easy decision to give.
Tierney has the most high-profile job of the match-week as he leads VAR for Manchester United's clash with Manchester City.
Meanwhile, Barrott has been named fourth official for Ipswich Town vs Wolverhampton Wanderers on Saturday and Tottenham Hotspur vs Southampton on Sunday.
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