The Dons moved a point ahead of the Hoops with a 2-0 win over St Johnstone on New Year's Day while Celtic's match away to Glasgow rivals Partick Thistle was called off due to a waterlogged pitch at Firhill.
Deila's side could find themselves four points behind in the title race before they take on Kilmarnock at Rugby Park on Monday if Aberdeen can defeat Motherwell on Sunday.
A defeat to Dundee United and a goalless draw with Ross County in their previous two matches means Celtic have dropped 15 points already this season - as many as the whole of the last campaign when the Hoops lost just once.
However, Deila, whose side have a game in hand over the Dons, pointed out that Celtic's fate remains within their own hands and is confident their experience means they can handle the pressure of a title race.
"Our players are used to fighting for a championship
They've been in this situation before
The last two seasons haven't maybe been so tight
But the club and the players are used to fighting for trophies, more than the other teams," Deila said.
"Aberdeen are not used to being at the top
It's always better to have the experience of being up there
Aberdeen have proved they can win a lot of games but we'll see if they can keep on winning.
"If we win our game in hand we will be two points ahead
We know what we have been doing is the best in the league but we have to keep progressing.
"It's going to be an exciting run towards the end of the season
Aberdeen are on a good run and that's why they are challengers.
"It is still in our hands, if we win all our games we'll be league winners.
"It is early though to start talking about it
There are 19 games left, 20 for us, so we'll see how things are when there's one month left."
- Stokes on sidelines -
Defender Efe Ambrose is also adamant that Celtic will go on to win their fourth title in a row once the players find top gear again.
"We know how the gaffer wants us to play and the level he wants us to be at, and we're not there yet, but we're working hard to get there, and I know that when we get to that level, we'll go on and win the league," the Nigerian said.
"We know we've not been at our best recently and we've not been converting the chances that we've been creating, so we've been training hard and working hard to improve, and I think you'll see that against Kilmarnock on Monday night."
The Hoops could welcome back winger James Forrest and defender Jason Denayer for the match at Rugby Park but striker Anthony Stokes will miss out along with Mikael Lustig and Charlie Mulgrew.
Elsewhere, United can provisionally go above Celtic with a win at Partick on Sunday, while Hamilton can move level on points with the champions with a win at St Johnstone.
Inverness in fifth entertain St Mirren and bottom club Ross County go to Dundee, who have not won any of their last seven league matches.
Fixtures (1500 GMT unless otherwise stated)
Sunday
Dundee v Ross County, Inverness Caledonian Thistle v St Mirren, Partick Thistle v Dundee United, St Johnstone v Hamilton Academical, Motherwell v Aberdeen (1530 GMT)
Monday
Kilmarnock v Celtic (2000 GMT)
Source : AFP
Source: AFP