The Scottish champions came back from two down in the first half after early strikes by Xherdan Shaqiri and Rodrigo Palacio with goals from midfielder Stuart Armstrong and an own goal from Inter defender Hugo Campagnaro within the space of a minute.
Hoops keeper Craig Gordon, so often a saviour for the Parkhead side since signing on a free last summer, had looked at fault for Inter's opener and another mistake a minute from the break gifted Palacio his second.
Guidetti, on loan from Manchester City but who had fallen out of favour recently, came on for Leigh Griffiths with 15 minutes remaining and in the third minute of four added on, slammed the ball high into the net to send Parkhead into raptures and have everyone looking forward to the second-leg of the last-32 tie in the San Siro next Thursday night
Deila said: "It was an unbelievable football match with and an unbelievable atmosphere
I am so proud of the players
"We went two down early in the match, it is so hard to get back, especially against an Italian team, but we have talked about being brave, wanting the ball, trying to attack and that is why I am very proud because we caused them problems and got an result in the end
"We wanted a better one and could have if we didn't give them two easy goals."
However, that was as far as the Norwegian would go in regards any criticism of Gordon.
He said: "We wouldn't be here if it wasn't for him
We would have a Thursday off.
"He was unlucky
The fans called his name and I appreciated that."
Guidetti, who had worked under Inter Milan boss Roberto Mancini at Manchester City, has been left on the bench in recent weeks in the midst of a goal drought but Deila claimed the Swedish striker was ready to get back on track.
He said: "I said early in the week that he was in good focus and he trained well and when you train well you get the results.
"He played well when he came on and got a good goal as well."
The former Stromsgodset boss is looking for another tough game in the second leg in the San Siro next week.
He said: "It is going to be very tough.
"We will need a bit of luck and to put in the best performance of my time here.
"But (it is) possible and we are looking forward to it.
"I believe we can score in the San Siro but we have to better defensively."
Mancini claimed his side thought it was too easy after going two goals up early in the game.
He said: "We started the game well but it wasn't good enough.
"We scored two goals and after this we thought it was an easy game.
"We were never finished and we took our chance to come back into the match but Celtic are a good team who play good football.
"I am not surprised at the result
We know that the game is 95 minutes and with one mistake the result can change.
"I think that we can start the next game with a slight advantage but we will need to play very well."
Armstrong, who made his home debut and also his European bow for the Hoops along with fellow new signing Gary Mackay-Steven, praised Adam Matthews for setting him up for the first goal and also looked to take the credit for Celtic's second.
He said: "It was great play by Adam Matthews, he put it on a plate really so I couldn't miss.
"It was a great team effort, a lot of hard work and I'm just so happy that we got something out of the game."
Asked if he was claiming the second goal, he said: "Of course, yes
I thought I'd celebrate anyway, I managed to get a nick on it and I think it went in off him but I'll take it.
"Games like these are why I came to Celtic
I've never experienced it before, the noise levels were incredible and it's something that every player wants to taste
I'd love more of it.
"We've shown tonight we can cut them open, we created a lot of chances and could've scored a couple more.
"To do that against such a well-known team gives us a lot of confidence and optimism going over there."
Source : PA
Source: PA