The reigning Premier League champion faces the prospect of being without the centre-back for the majority of the season after he damaged knee ligaments during the Merseyside derby.
Van Dijk was caught by a heavy challenge from Pickford in the early stages of the game at Goodison Park, though the England international received no punishment from the officials - both those on duty at the game and also the video assistant referee watching on from afar - following the incident.
Liverpool midfielder Georginio Wijnaldum branded the tackle as "completely stupid" before the Champions League game with Ajax in midweek, but Ancelotti has defended his player.
Speaking ahead of Everton's game at Southampton, the Italian wished Van Dijk well in his recovery from surgery but made clear any suggestions of premeditation on Pickford's part are wide of the mark.
"To be clear, we are really sorry for the injury of Virgil van Dijk," Ancelotti told EvertonTV. "Every one of us hopes he can recover soon and well.
"There was this contact with Jordan Pickford: it was mistimed contact. But the fact the Premier League is so fast, it is not so difficult to arrive a little bit later.
"Jordan arrived a little bit later but his intention was to try to reach the ball. It was not to hurt Virgil van Dijk.
"To say it was premeditated, and this and that, in my opinion, is too much. Virgil van Dijk knows this.
"Jordan is really sad, really disappointed [that Van Dijk is injured]. It was a strong contact, maybe mistimed, but sometimes in football it can happen."
Ancelotti also revealed that James Rodriguez is set to miss the game against the Saints with an injury suffered in a challenge with Van Dijk before the Dutchman was substituted.
Both James and captain Seamus Coleman - who came off during the 2-2 draw with the Reds - are likely to sit out Sunday's trip to the south coast, though Jonjoe Kenny is available again.
"Unfortunately, James had a problem during the game [against Liverpool]," Ancelotti said.
"He had a mistimed tackle with Virgil van Dijk at the beginning of the game and I think he will not be available for the game against Southampton."
James has been outstanding since moving to the Premier League from Real Madrid, scoring three goals and providing a trio of assists for his new employers.
The Colombian playmaker has created 15 chances in total for his team-mates, while also completed 87.55 per cent of his attempted passes.