Manager Ronny Deila had targeted the treble in his first season but that dream ended in controversial fashion with a 3-2 William Hill Scottish Cup semi-final defeat by Inverness on Sunday.
Deila started with a disastrous Champions League qualifying campaign when Celtic were knocked out by both Legia Warsaw and Maribor, but went on to impress in the Europa League and domestic scene with the League Cup already in the trophy cabinet following an absence of six years.
And Van Dijk is now looking to wrap up the title in style to get over his Hampden disappointment.
Celtic can reopen an eight-point lead over Aberdeen by winning at Dundee on Wednesday night ahead of the post-split fixtures.
“If we win the league we still improve from last year,” Van Dijk said. “We want to win it as soon as possible and that starts on Wednesday.
“The disappointment is very high, everybody is down but we are professionals and we need to focus on Dundee.
“We need to move on. Wednesday night at Dundee is a big game, so we need to be ready for that.”
Celtic striker Leigh Griffiths accused the match officials of robbing them a cup final appearance after they failed to spot his goal-bound header being stopped by the hand of Inverness defender Josh Meekings when the Hoops were leading 1-0.
But Van Dijk refused to dwell on the blunder by referee Steven McLean and additional assistant Alan Muir, who was five yards away.
When asked about the penalty claim, the Dutch defender said: “It didn’t happen so we can’t talk about it.
“We look at our own performance and we lost and we are not on for the treble anymore.
“It should have been a key moment but it didn’t happen so there is nothing to talk about. We lost and we are very disappointed.”
Van Dijk opened the scoring at Hampden when he curled a free-kick in off the post but himself and Jason Denayer were given a tough afternoon by the pacy Marley Watkins and powerful Edward Ofere, who scored Caley Thistle’s second goal.
“We gave everything,” he said. “With 10 men we kept on fighting. We had quality to score a goal but unfortunately it wasn’t enough.”