The Irishman was gutted as his side lost out 4-1 to Hamilton at the weekend, a result which threw the battle for fourth place wide open – and saw Hibs miss out on a chance to close the gap on third-placed Dundee United to five points.
However Motherwell lost out 2-1 to Celtic at Parkhead last night, meaning they remain two points behind the Easter Road side having now played the same amount of games.
With matches against the Steelmen and United to come in the weeks ahead, Cregg believes the fight for a Europa League spot is still in Hibs' hands and he said: "Getting a European place this season would be a massive boost for everyone.
"We have got to make sure we stay in at least fourth, and keep pushing for third as well. I know is going to be extremely hard but that's what we have got to be aiming for.
"We have still got Dundee United and Motherwell to play before the end of the season and we have got to make sure we beat Hearts in the final derby game as well.
"It would be a real kick in the teeth if we didn't get fourth place but we can only blame ourselves if we don't.
"The manager is sending us out to win games still and is doing a very good job of keeping us motivated and determined to finish in at least fourth position."
Having spent much of the season out of the side, the first-team door opened for Cregg again last month when he came off the bench late in the game against Falkirk to replace Anthony Stokes.
He played the full 90 minutes of the following matches against Dundee United and Celtic, and, despite taking a knock on his foot against the Parkhead side, managed to start Saturday's game at Hamilton.
The Irishman lasted almost 70 minutes before having to admit defeat to that foot injury and conceded he may have been wiser to sit the match out but he was desperate to continue his run in the first-team.
He said: "I took a knock against Celtic and maybe I shouldn't have played against Hamilton.
"I took a kick on my foot and it kept me out of training for a few days but I was back before the end of the week and I thought I could get through it with adrenalin but I maybe needed to give myself that bit more time because I didn't play great."
Cregg hasn't trained this week as a result of that injury but is hopeful of taking on Neil Lennon's side this Saturday: "I will hopefully be fit for selection by the time Saturday comes.
"I haven't trained all week but I'm hoping to get involved over the next day or two and be fit for Celtic Park because it's a great place to play.
"I let myself down on Saturday, I was really disappointed with myself on a personal basis but, with hindsight, I probably shouldn't have played because I wasn't 100 per cent fit.
"I'll just have to learn from that kind of mistake and move on.
"I've been in and out of the team this season and I wanted to give it my best to try to stay in the side."
The closing stages of Hibs' heavy defeat at New Douglas Park saw fed-up supporters chant that they "wanted their money back".
With three of their final five SPL games to be played away from home, Hibs will be relying on travelling fans for vocal backing as they bid to keep their Euro hopes alive. And Cregg, who believes the fans have the right to voice their views, added: "I wouldn't say that the fans have been giving us a hard time – the last few results haven't gone our way and we've not played too well either.
"If they think that we should be doing better then they are entitled to their opinion, they pay good money to go to these games.
"But I think our supporters have been great and the away fans are always brilliant.
"I am sure they will be there again on Saturday and in the rest of the games that are left this season.
"We will all be doing our best to get the team as high up the table as possible because all of the lads understand that when you are playing for Hibs, you are playing for the whole community. We want to do the best that we possibly can for us and for them.
"When you play you just try to focus on the game and shut everything else out anyway and the main thing for us is to minimise our mistakes."
The Hibs players must now lift their spirits in time for this weekend's trip to Parkhead and Cregg admitted the absence of the suspended Liam Miller is a huge blow to the Easter Road side. He said: "The mood has been good this week but we are eager to get the next few days out of the way and play the game against Celtic. The manager has done a good job of picking all of the lads up and getting us focused on Saturday and the remaining games of the season.
"We know how important it is to try to push into Europe. There are some hard games coming up and I think that, just by the nature of the top six, everyone is going to drop points somewhere along the line. We need to get as many in the bag as we can and we'll be going into every game that we play to try and win it. Liam is suspended but it has maybe worked out okay for us because I think he's been carrying a bit of a knock anyway.
"Either way, it is a massive blow for us to lose someone with his experience from the side.
"At the moment, I think we need to show a lot of determination. We have to show our hunger and the next five games are all big ones – there's no excuse for us not being up for them.
"We will most definitely be raring to go come Saturday."