A thumping 6-2 victory at Everton lifted Spurs back to within six points of leaders Liverpool and only two behind Manchester City, but Pochettino believes they still have some way to go to be in that race.
The Argentine has been heavily linked with United following Jose Mourinho’s sacking, but he stressed Spurs were concentrating on keeping the pressure on the leaders.
“Talking about rumours, there are a lot of rumours,” said Pochettino.
“This guy [Spurs’ press officer] became upset again or angry [by questions about United], but we cannot talk, we need to be focused on our jobs at Tottenham and do our best to try to be successful.
“I still believe Liverpool and Manchester City are the real contenders and favourites to win the Premier League.
“We are there, but [so are] Chelsea, Arsenal and Manchester United. I think there is still a long way for me to say we are real contenders.
“Football is about being consistent of course. If we are able to be consistent and play in the way we did tonight I think yes maybe we could then be a real contender, but there is still a long way.
“Being involved in four competitions will be tough, but we are going to try.”
Harry Kane, equalling a Premier League record held by Michael Owen by scoring twice in four successive matches against one opponent, and Son Heung-min both bagged braces, with Christian Eriksen and Dele Alli adding the others.
However, Spurs lost Alli at half-time to a hamstring injury after visibly frustrated Everton keeper Jordan Pickford – who was at fault for Spurs’ opener – clattered him after the whistle when his England team-mate put the ball through his legs.
Pochettino was unhappy with the challenge, but was not prepared to condemn it until he had watched a replay.
“I didn’t see. I am very curious to see the action, I think it wasn’t a great action,” he added. “I don’t want to say anything because I didn’t see it. For some comment I think it was a tough action.
“We will see if he is injured. I think he is tired and it is a tight hamstring, but we hope it is not a big issue.”
Everton took the lead with Theo Walcott’s first league goal in four months, but, after Gylfi Sigurdsson briefly made it 4-2, they fell apart.
It left Marco Silva with plenty of questions to answer, with his side in 11th place with 24 points, a worse position than at Christmas last year when they were ninth with 26 and on their third manager, Sam Allardyce, having dispensed with Ronald Koeman and caretaker David Unsworth.
The Portuguese, however, felt the disallowing of Dominic Calvert-Lewin’s header with the score at 1-0 was pivotal. “Really bad afternoon for us, really bad result for us as a team and our fans,” he said.
“We have to realise why and we will for sure. We started the match well and we scored.
“We scored a second goal, in my opinion, but talking about the ref is not my way and I don’t look for excuses. I didn’t see nothing, the match would have been really different.
“We made the first mistake in the match when they equalised and the game changed completely.”