Demba Ba scored the only goal as the Stamford Bridge outfit battled to a 1-0 victory at 10-man Swansea City on Sunday, leaving them two points adrift of leaders Liverpool, who were 3-2 winners over Manchester City earlier in the day.
Chelsea are set to visit Anfield in two weeks' time, and Holland - who was asked by manager Jose Mourinho to take the post-match press conference - feels that the defeat at Crystal Palace last month has left them needing a perfect run-in to stand a chance of being crowned champions.
"It looks like being an exciting conclusion to the season for everybody," he said. "I think we've probably got to win all of our games one way or another. That's the likelihood.
"We've been facing that task now for probably a good couple of weeks, certainly on the back of our result at Crystal Palace.
"I think any leeway we had was eliminated after that result."
And Holland confessed that the players had been aware of the result in the day's early kick-off.
"No matter how much you try and hide it and take the players' minds away from it, in this world of technology that we live in now, there's always a way of somebody finding out at some point," he continued.
"So we were aware as the afternoon progressed. It is something that the players have to handle and is normal in this kind of situation."
Swansea head coach Garry Monk questioned the dismissal of defender Chico Flores in the first half, alleging that Chelsea's players and coaching staff tried to exert some influence over referee Phil Dowd, but Holland believes that the official made the correct decision.
"In my opinion, the two yellow card decisions were crystal clear." he stressed. "I've seen them both back and I think the referee was correct on both counts.
"The referee made the decision and he made the decision correctly."
Eden Hazard was absent for the match after picking up a calf injury as Chelsea beat Paris Saint-Germain in the UEFA Champions League on Tuesday, but Holland had some positive news for the club's fans.
"Eden should be sooner rather than later," he added. "It's a little bit too early to say for sure."
