The Italian head coach, who is under contract at Stamford Bridge until the summer of 2019, oversaw a 1-1 draw with Barcelona in the Champions League on Tuesday night.
The Blues won the Premier League under Conte last season but for much of this term he has faced questions about his long-term future with Chelsea.
Speaking to Italian TV channel Mediaset, Conte said: “It’s partly to do with the history of Chelsea, it’s unavoidable.
“In the past 14 years there have been 10 changes of manager. Clearly when there is — and I say this in quotation marks — that kind of custom then the press play on it a lot, especially when results don’t materialise.
“This year there’s been a lot of pressure... after the first defeat to Burnley there were people talking about the sack and about a change on the Chelsea bench but that’s because of the history here.
“Chelsea are talked about a lot by the press but for me that’s absolutely not a problem. I just hope that pressure doesn’t affect the players, whereas I like pressure.”
Conte has been linked with a return to the position he held before taking over at Chelsea, that of Italy head coach. The post remains vacant following Giampiero Ventura’s resignation following Italy’s failure to qualify for this summer’s World Cup.
Conte, however, insists he is fully committed to Chelsea.
“I’ve said this in a very clear way, I have a contract with Chelsea until 2019 and I intend to respect that contract.
“As with a marriage, both parties need to be happy, yet in this profession we always have our suitcases ready. But my intention, I repeat, is to respect my contract here at Chelsea.”
The Blues face an uphill struggle to reach the Champions League last eight but Willian, their goalscorer at Stamford Bridge, is confident they can pull off a shock win in Barcelona next month.
Willian came close to upstaging Argentina superstar Lionel Messi in the first leg, firing the Blues into the lead having previously twice been denied by a post. However, Messi had the final word when he capitalised on a rare Chelsea defensive error to bag his first goal against the west Londoners at the ninth attempt and secure a 1-1 draw.
Nevertheless, Willian saw enough in Chelsea’s performance at Stamford Bridge to suggest they can upset the odds in the second leg.
“In a difficult game we played very well,” he told the club website. “We had to stay compact, we had a plan and we did exactly as we expected.
“They had the ball and we expected to counter-attack, and we could win this game. But we did not and the result is still open, we have to go there and try to win. Barcelona had more possession but they did not create more dangerous chances to score.
“To play in the Nou Camp is totally different and we have go there with the same mentality and try to win the game.”
Willian may have put in a man-of-the-match display but the Brazilian knows he has to maintain that level as Chelsea’s season reaches a crucial stage.
The Blues now face back-to-back trips to Manchester, facing United - and old boss Jose Mourinho - on Sunday before heading to champions-elect City the following weekend.
“It was one of my best performances here,’ added Willian. “I almost had a hat-trick!
“We were a bit unlucky but we must be proud of our performance because we played really well.
“To play against Barcelona is not easy and now we have to think about the other games.
‘We go there in three weeks’ time and we have difficult games as well in the Premier League. Now we have to think about the games coming and then we have to think about Barcelona.”
Meanwhile Thomas Mueller was relieved Bayern Munich overcame a listless start to lay down a marker in their Champions League last-16 clash against Besiktas.
Bayern were given a shot in the arm after a quarter of an hour at the Allianz Arena when last man Domagoj Vida saw red for bringing down Robert Lewandowski.
However, the Turkish champions kept their goal in tact until just before half-time, when Muller’s goal presaged a second-half deluge.
Kingsley Coman and Mueller’s second moved Bayern further into the ascendancy while Lewandowski’s late brace wrapped up a 5-0 win that all but secured the German giants’ passage into the quarter-finals for the seventh successive season.
Mueller said: “The red card played right into our hands. We lacked aggression when we had the ball in the first half, we were a bit sluggish.
“It changed abruptly in the second half, we really hit the gas.”