Celtic have been paired with Partick Thistle in the last eight following their comprehensive win over the Championship league leaders.
And Deila says he is desperate to pick up some silverware in his first season in charge of Celtic after making a stuttering start which has seen his side win just six of their opening 14 matches.
"We are looking forward to the next game, whoever we meet," the Celtic manager said before the draw was made.
"We are comfortable that we are a very good team and whoever we are going to meet are going to have a big challenge."
Celtic, who made an embarrassing exit at this stage of the competition last season to Morton, made four changes from the side that could only draw with Motherwell at the weekend.
His decision to restore his first team stars paid off when John Guidetti fired Celtic in front midway through the first half as he grabbed his first goal since joining the Glasgow giants on loan from Manchester City.
Guidetti then won his side a 56th minute penalty which Kris Commons converted just two minutes after Osman Sow blazed his penalty for Hearts over the bar at the other end.
An Adam Eckersley own goal rounded off the scoring in the 61st minute.
Deila has come in for criticism after making wholesale changes following European matches which contributed to draws with Dundee and Motherwell and a defeat to Inverness Caledonian Thistle in the league.
However, the Norwegian manager hinted that he may stop tinkering too much with his side in the future in favour of a more settled starting 11.
"I think we had players who came in who did well and we had players on the bench who can do well
But I think it is important to keep more consistency in the team because if you change too much, as I've done twice, then we haven't played well and I can understand why," the Celtic boss said.
"I'm very pleased today as I think we're going in the right direction all the time now
What I'm most pleased about is we worked as a team with 11 players who wanted to win the ball.
"We also started to create things on the sides, especially with Anthony Stokes and Emilio Izaguirre and that's something to build on.
"My philosophy in football is we need to be very dangerous on the sides and also in the centre
Celtic have been good in the centre for many years now but I think to create what we want here then on the sides we can do better
Today we did well on the left side and we kept a clean sheet, which was good."
The Glasgow giants avoided a potential last eight tie with city rivals Rangers, whom they haven't faced since 2012 following the Ibrox club's financial collapse which meant they had to start life again in the bottom tier of Scottish football.
Ally McCoist's side, who came from behind to defeat fellow Championship side Falkirk 3-1, will instead host Premiership side St Johnstone who progressed to the last eight following a 1-0 win over Kilmarnock
Championship strugglers Hibernian's reward for a 2-0 win over Ross County was a home tie against Dundee United, who claimed a 1-0 win over rivals Dundee with a dramatic late header from Jaroslaw Fojut
Holders Aberdeen continue the defence of the League Cup at home as they welcome Hamilton, who knocked Lanarkshire rivals Motherwell out on penalties, to Pittodrie.
Source : AFP
Source: AFP