Everton and Newcastle finished their pre-season schedules with defeat, while Wolves won on a busy Saturday of warm-up action.
Richarlison and Lucas Digne made their Goodison Park debuts in a game that was Marco Silva's first in charge in the home dugout but despite twice coming from behind against Valencia, the Toffees were pipped 3-2 by the La Liga side.
Cenk Tosun (19) and Michael Keane (29) had restored parity after Rodrigo Moreno's double (9, 24) but Daniel Wass struck a long-range winner for the Spaniards 15 minutes from time.
Silva was animated throughout a contest that exposed some defensive frailties but Theo Walcott came off the bench for his first appearance of pre-season, while Dominic Calvert-Lewin had a second-half run-out.
Alisson made his debut for Liverpool and Mohamed Salah got on the scoresheet as the Reds beat Napoli 5-0, while Arsenal were also 2-0 winners against Lazio. Tottenham fell to a 4-1 defeat to La Liga side Girona in Spain.
Newcastle were thrashed 4-0 by Braga in midweek and the Magpies signed off pre-season with another loss after Michael Gregoritsch earned Augsburg a 1-0 win at St James' Park.
Rafa Benitez's side had dominated against their German guests but failed to find a breakthrough and were made to pay when Gregoritsch beat Karl Darlow with a 61st-minute header.
Wolves signed off their pre-season preparations with victory after coming from behind to beat Villarreal 2-1.
Gerard Moreno had put the visitors in front at Molineux but though Ruben Neves spurned a penalty, quick second-half goals from Willy Boly (49) and Raul Jimenez (55) sealed a comeback victory.
Meanwhile, Crystal Palace enjoyed a 4-1 win at home to Toulouse. Aaron Leya Iseka (10) had given the hosts an early lead, but goals from Christian Benteke (29) and Jeffrey Schlupp (33), as well as a Luka Milivojevic penalty (39), turned the game on its head by full-time.
Wilfried Zaha (81) scored the only goal of the second half as the Eagles geared up for their Premier League opener at Fulham in style.
Bournemouth also finished their warm-up campaign on a winning note, thrashing Marseille 5-2 at the Vitality Stadium.
Eddie Howe's raced into a 5-0 lead against their French opponents, Adam Smith finishing a kick-off routine with just 13 minutes on the clock.
Josh King scored twice (25,35), before Ryan Fraser (47) and Callum Wilson found the target in an impressive attacking display, though Marseille did muster consolation goals through Valere Germain (64) and ex-Newcastle player Remy Cabella.
Aleksandar Mitrovic scored and claimed an assist as Fulham drew 2-2 with Celta Vigo at Craven Cottage.
The striker, signed permanently from Newcastle, struck with just two minutes on the clock and set up Aboubakar Kamara (16) after Dennis Eckert had headed the visitors level.
Gustavo Cabral restored parity from a free-kick four minutes before the break and though a winner proved elusive, Jean-Michel Seri and Andre Schurrle impressed for Slavisa Jokanovic's side.
Elsewhere, Watford came from a goal down to draw 1-1 with Sampdoria in a game played in tribute to the late Graham Taylor.
The Hornets unveiled a statue in honour of their greatest manager ahead of kick-off, before Troy Deeney (53) cancelled out Omar Colley's eighth-minute opener.
Leicester tasted victory ahead of their Premier League opener against Manchester United on Friday Night Football, recording a 2-1 win in Lille.
Claude Puel's side fell behind to an early Lebo Mothida goal (4), but two goals from Kelechi Iheanacho (34, 59) turned the game around - the Nigeria international now with four goals in three friendly games.
Cardiff City fell 2-1 at home to Real Betis. Despite taking an early lead thanks to summer signing Josh Murphy (4), the La Liga side recovered to earn the victory after goals from Loren (22) and Cristian Tello (30).
Southampton were well beaten in their final warm-up fixture, Borussia Monchengladbach earning a 3-0 win at St Mary's.