The Hoops crashed out of Europe altogether after Tuesday's 3-0 defeat by AC Milan ensured they will finish bottom of Group H.
But Celtic were responsible for their own downfall as they all but gifted their opponents the three goals.
Defender Virgil Van Dijk could have levelled the match at 1-1 shortly after half-time but blew his big chance when he volleyed straight at the Italian's keeper Christian Abbiati.
However, Locke believes his side are capable of living with the reigning champions when they meet in the William Hill Scottish Cup fourth round at Tynecastle.
The Hearts boss - who was overjoyed to see his club take another step towards exiting administration on Friday when creditors voted in favour of a Company Voluntary Arrangement - said: "Celtic will be under more pressure than we are. They are the holders and the SPL champions and have a fantastic team, whereas we have a very young side.
"But I felt we played really well against them earlier on in the season and if we can show that same character and commitment hopefully we will give ourselves a chance.
"But I don't think the pressure will be ramped up further on them because of their European exit.
"I was at the game on Tuesday night and I thought they were really unlucky. The big boy Van Dijk missed a great chance and if he had scored that one, it would have been a completely different outcome.
"But they more than matched AC Milan, as they have done with every other team they have faced in the Champions League.
"That shows the quality Celtic have got. But it is up to us to go out and compete with them and show what we are good at. If we can, maybe we can get the right result."