Pochettino pleased with new-look Chelsea, Klopp takes positives for Liverpool
The visitors settled into the new season quicker at Stamford Bridge and could have been out of sight inside the first 30 minutes.
Mohamed Salah hit the crossbar before teeing up Luis Diaz to open the scoring.
Salah then saw a second goal ruled out after a VAR review for offside.
But the momentum swung back Chelsea's way after debutant Axel Disasi equalised eight minutes before half-time.
VAR intervened once more to deny the Blues a second when Ben Chilwell scored and the home side wasted a series of chances to secure three points after the break.
Pochettino took over a side that had finished 12th last season - Chelsea's lowest finishing position since 1994.
And the Argentine believes they will only improve as the season goes on.
"Fantastic way to start the season, unbelievable game," said Pochettino, who previously managed Southampton and Tottenham in the Premier League.
"Overall I think we deserve a little bit more. We feel pleased and at the same time disappointed.
"That is only the beginning and I am so pleased with the performance of the players."
Chelsea and Liverpool have spent recent days battling for the signing of Brighton midfielder Moises Caicedo for a Premier League record fee.
Liverpool had a £110 million offer for the Ecuadorian accepted by the Seagulls, but the player appears to be holding out for Chelsea and Brighton to agree a fee.
"If we want to be a contender we need to improve in all areas," added Pochettino.
"It's time to work all together, once the transfer window closes, to find the best dynamic. This result makes us believe, that is why I am positive."
Liverpool are in even more desperate need of midfield reinforcements after losing captain Jordan Henderson and Fabinho to the wave of players heading to the Saudi Pro League.
After a bright start, the Reds' defence was easily picked apart with an attack-minded midfield offering little protection.
"The start was pretty convincing," said Liverpool boss Jurgen Klopp. "We scored two wonderful goals, one was disallowed for an offside.
"We opened up the door for Chelsea, we lost the ball in moments where it was difficult to prepare for it. It gave the game a different direction, so we were not in control of the game."
However, Klopp insisted he is still "really looking forward" to the season ahead.
Liverpool are aiming to bounce back after missing out on Champions League qualification last season for the first time in seven years.
"Today didn't decide where our season will go, it's just important information," added Klopp. "This team deserve so much trust, they will go for it!"
Meanwhile, Salah, who is tied with Alan Shearer, Wayne Rooney and Frank Lampard for most goals scored on opening day, appeared unhappy with the substitution, peeling the tape around his wrists and throwing it to the ground, but Klopp played down the significance of his reaction.
"I didn't have a conversation yet with him," Klopp said. "I did not know that if he could have scored in that game it would have been an all-time record or whatever.
"I understand his disappointment, but I'm the manager of the whole team. In that moment we needed fresh legs, (the substitution) made sense for us.
"It was super intense for everybody. That's all I can say about it, his reaction was absolutely okay."