"We've got good players to work with and at the moment we've done really well to get to the quarters and challenge for top four, but we've got a rebuilding job", he admitted.
Ronaldo, meanwhile, shook his head as he walked off the field, while the Ajax players and staff celebrated with their fans long after the final whistle following a 2-1 win in Turin that sealed the Dutch side's first semi-final appearance since 1997.
Jesse Lingard was candid after the match and recognised individual errors cost United at the Nou Camp.
Ole Gunnar Solskjaer has sent Manchester United's executive vice-chairman Ed Woodward a message after the defeat to Barcelona.
Valverde was predictably delighted with Messi, who is up to 45 goals in all competitions this season.
They could have hardly have asked for a better start.
At one stage his distribution in the second half had dipped to 82.5 per cent - six team-mates in Blaugrana blue and claret were into the 90s (goalkeeper Marc-Andre ter Stegen had 100 per cent) - with Coutinho closest to him with 84.9 per cent.
His first goal, Barcelona's opener, was such a blow for United as they struggled to mentally recover, as shown by De Gea's mistake for Messi's second minutes later.
Barca were flustered, so much so the crowd even cheered with relief when Arthur Melo played his team's first convincing pass.
But United's early pressure almost turned to despair when the referee pointed to the spot and awarded Barcelona a penalty for Fred's challenge on Ivan Rakitic. Young lunged in to atone for his mistake but Messi skipped away from him, poked it through Fred's legs and then whipped the ball into the corner.
The second was simpler.
"At 2-0 straight after it was game over".
Sergi Roberto at the far post only for De Gea to redeem himself with a fantastic save.
Rashford might have made it interesting if he had controlled Pogba's ball over the top but Barcelona were in exhibition mode, helped by a vintage Coutinho curler after he had cut inside from the left. Barca's less so, especially in recent years where they have had to take a back seat to fierce rivals Real Madrid's trailblazing antics in Europe.