The Bhoys defender knows the league champions haven't been at their best lately.
Ronny Deila's men will still top the SPL table if they win their game in hand but are without a win in two (and had their league clash with Partick Thistle abandoned yesterday).
But Ambrose admits Celtic have to improve - although he is confident that is exactly what they will do.
"We have to show a winning mentality. We know we've not been at our best recently and we've not been converting the chances we've created," Ambrose told reporters.
"So we've been training hard and working hard to improve and I think you’ll see that against Kilmarnock on Monday night.
"We have to have the character because being a Celtic player brings great responsibility and we know what that means.
"I think the best is still to come from us. We know if we win every game between now and the end of the season then we’ll win the league.
"Aberdeen are top just now and they've played well so we respect them and they will provide a challenge, as will Dundee United."