The Chelsea midfielder was part of a double substitution shortly into the second half, including Eden Hazard, which immediately paid dividends as the Blues fought back quickly to make it 2-2.
Mikel said: "We went into the dressing room and had a little chat and we came out into the second half and started to show a bit more character and belief that we can actually come back into this game.
"All we needed was to score one goal and then hopefully the belief will come in and then hopefully we can get a second one and that's exactly what we did."
Despite the promising display the Nigerian said they still have it all to do in the replay at Stamford Bridge.
He added: "This tie is not done you can never write off Man United at any time so we have to go back in London and make sure we put it away."
Chelsea will play Man City in the semi-final if they beat United.