However, the former Gers defender suspects a decision will not take place until the end of the campaign.
Asked whether the Bhoys would part company with Deila after the Old Firm defeat, Butcher told the Alan Brazil Sports Breakfast show on Monday: "I think they will do. I think they'll probably leave it until the end of the season and take some action.
"It (Sunday's defeat) was so disappointing for Celtic fans."
Deila is on a rolling 12-month contract at Parkhead, making his departure far more straightforward than it would be under a longer agreement.
The Norwegian is under growing pressure despite a fifth-straight Premiership title on the horizon and faced strong criticism in the aftermath of Sunday's penalty shoot-out defeat at Hampden Park.
Butcher, however, cited Rangers' unpredictability as the reason for Celtic failing to live up to their favourites tag and said Deila "did his work" on the day.
"Well he did (do something about it) at half-time," added the former Motherwell, Inverness and Hibernian boss. "He certainly got a reaction from his players at half-time and at half-time in extra-time too so you could say he did his work there. But I think Rangers took Celtic by complete surprise."
Rangers were ahead at both intervals but equalised five minutes and one minute after each, through substitutes Erik Sviatchenko and Tom Rogic respectively.
The two sides will compete in the top-flight next season, and the Light Blues are looking to make an immediate challenge for the title according to manager Mark Warburton.