After the game, Van Dijk accepted the referee was right to point to the spot and expressed his relief that the incident did not cost his team - as Riyad Mahrez sent the kick over the crossbar.
And City could have secured victory after being awarded an 86th minute penalty when substitute Leroy Sane was brought down in the box.
City had the flawless opportunity to end their awful run at Anfield but Mahrez, not particularly reliable from the spot, blazed his effort high into the stand.
The change of position seemed to have a destabilising effect on the 21-year-old, who diverted Lovren's header back to Sergio Aguero in the penalty area.
This, as Guardiola explained after the game, was part of City's game plan, with the visitors looking to stymie Liverpool's swift counter-attacking play after losing twice at Anfield last season.
In a game that saw little goalmouth action, City edged the midfield battle and could have been rewarded all three points via a late 86th minute penalty.
"It was a great game to play obviously and it's unlucky that we didn't score and unlucky [for City] that we didn't concede as well". Also, City have lost just one of their last 25 away games in the top flight, and they are yet to taste defeat in the PL this term.
The Merseyside outfit came from behind to rescue a 1-1 draw with Chelsea FC at Stamford Bridge last weekend after former Manchester City striker Sturridge netted a late equaliser.
"When we came back from the global break last time, it was clear", he said.
"I am really happy with what the boys did today", Klopp said. "We were close, more than ever to winning here but it is better than last season when we lose and especially when we try to be ourselves all the time", he added. "It will be a good experience for him, next time it will go in".
There was an early surge from Liverpool, and for seven or eight minutes at the start of the game, City struggled to deal with the ferocity of the Liverpool press, but once that storm had passed, City was relatively comfortable. They will have their moments, but I thought we defended them brilliant - apart from the penalty and one or two situations, where we needed Alisson with a really good save.