Speculation about the Celtic manager's future intensified after the home goalless draw against Dundee in midweek cut the Hoops' lead over Aberdeen at the top of the Ladbrokes Premiership to four points, and brought a crescendo of boos at half-time and full-time.
Only 14,858 fans turned up for the quarter-final tie against the Championship side to see Celtic win comfortably with first-half goals from Leigh Griffiths, Gary-Mackay-Steven and Callum McGregor.
The home supporters inside the 60,000-capacity stadium showed their appreciation after the game and Deila hopes the result and performance can help rebuild the trust.
The Norwegian said: "It is much better to get applause than a boo, that's for sure.
"Hopefully that is going to continue.
"We could have played without any fans because it is about loving playing football and we wanted to bounce back after a performance we weren't happy with.
"But I think the fans here were good
They stood behind the team and I was happy with that.
"They were happy afterwards, I recognised that and it was something to take with us.
"We have to build up our trust with the fans and they will support us even better, it is a win-win situation."
Asked if he felt any more pressure going into the game, Deila said: "I get that question every week
No I didn't feel that
"I am my biggest critic here and I have been in this game a long time.
"When everything is crazy around you, you have to stay calm.
"It is a game of football and we have everything in our hands.
"The players are winners, they hate losing and performing badly and they wanted to show the other side today and this is something we want to build on.
"It is our fourth semi-final in two years
We have two games left to hopefully lift a trophy
We will take what is in front of us," added Deila, who is hopeful the ankle injury picked up by Stefan Johansen just before the break is not too serious,
Mackay-Steven, meanwhile, was also pleased to hear cheers instead of jeers from the fans.
The former Dundee United winger said: "It was great, they haven't had a lot to cheer about in recent weeks.
"Today it was nice to score three goals and play a bit better.
"There is always pressure at this club but after drawing a few games you feel that a little bit more.
"We will take anyone (next), the main thing is getting our name in the hat."
Morton boss Jim Duffy was pleased with the way his side kept going after the break when the tie was effectively over.
He said: "I was disappointed in the first couple of goals, Celtic have enough quality to create and score goals without us handing them to them, and we gifted them the first two.
"They won the game relatively comfortably and I can't deny that but from my point of view we were organised as best we could be, we worked really hard and there was a terrific attitude from the players.
"We asked them at half-time to show a bit of bottle and character and not capitulate and although we got one two breaks when Celtic hit the woodwork, I thought they stuck to their task very well and they deserve a bit of credit for not throwing the towel in."
Source : PA
Source: PA