Spurs swept Watford aside at White Hart Lane this afternoon, courtesy of a 4-0 scoreline, to maintain their unbeaten home record.
The north Londoners are now just four points adrift of Antonio Conte's side, who travel to Bournemouth this evening.
And Pochettino is adamant he and his players are aiming to continue asking questions of their rivals as they attempt to overhaul the Blues with just seven games left to play.
"The message is to try and keep pushing - that is our job. What happens with Chelsea this afternoon is their problem.
"If they fail we are there. It is up to them to win the Premier League," Pochettino insisted.
Spurs made light work of the Hornets, with Dele Alli, Eric Dier and Heung-min Son all on target before the interval.
Son also fired home after the break to end the game as a contest, allowing Pochettino to ease Harry Kane back into action.
The Argentine coach believes his side are stronger after coping well during their talisman's absence but remains keen not to get too carried away as the finish line approaches.
Pochettino added: "From the beginning it was a tough game - they were very motivated to play us. But after 15-20 minutes we started to control the game. We dominated and fully deserved all three points.
"We must be focused on the next game. If not you do not spend time in reality. We must be ready for Bournemouth, be patient and work hard."