Deila gave a scathing analysis of referee Ivan Kruzliak’s performance in the San Siro, with the decision to give Van Dyke his marching orders especially disappointing the Norwegian.
The Scottish champions were more than holding their own until the Dutch defender was sent off in the 36th minute after picking up the second of two yellow cards, the first for a foul on Rodrigo Palacio, the next for tangling with Mauro Icardi.
It was an uphill task for Deila’s side thereafter and although they battled hard, Fredy Guarin fired in a wonderful strike with two minutes remaining to cap a frustrating evening for the Scottish champions.
“He had a bad day at work, that’s for sure,” Delia said.
“If we had that bad a day we would have lost 6-0.
“There were things that happened in the game that ruined it for us.
“It was very even when 11 against 11. We defended well with 10 men but couldn’t create anything.
“I feel sorry for the team – but very proud of the boys. There was a very good chance to go through and I think we showed that we have something at this level.
“It was an open match until the sending-off. It made it very difficult for us, we had to work hard in defence.
“Hopefully, we could have kept it going and got a chance near the end but we didn’t make it.
“Inter are a good team so we have to get over it and start focusing on what is going to happen on Sunday.”
Deila was referring to the visit of second-placed Aberdeen in a match which will go some way to deciding the destination of the title.
The champions are three points clear of the Dons with a game in hand and they face Dundee United in the William Hill Scottish Cup quarter-final and Scottish League Cup final next month as the quest for the domestic treble continues.
The former Stromsgodset boss said: “It was a good performance and give us motivation for domestic football so we can hopefully get back to the Champions League next season.”
The Parkhead club were fined 10,000 euros by UEFA on Wednesday for crowd disturbances in the game against Dinamo Zagreb in Croatia last year and they could be in trouble again after two flares were held up in the section housing around 3,000 Hoops fans.
Deila described it as “very disappointing” and said: “We have to get rid of this, this is is nothing to do with football.
Again the fans were unbelievable, you can hear the fans still singing now, that is important for us but again we have to behave in the right way.”
Roberto Mancini admitted Van Dijk’s dismissal gave his side an advantage but insisted they had the game in hand.
“It made our life easier but we had the chances to score before that,” Mancini said.
“We managed the game in the right way.”