Just three minutes before the final whistle, Liverpool almost took the lead through Solanke, who was unlucky after his effort was denied by the woodwork.
However, as fans begin to write off the Reds' Premier League title chances, maybe they'll have more luck in 2017-18?
Liverpool return to Premier League action next weekend with a trip to Leicester City in the Premier League.
"I think he might be limited to chances at Liverpool but obviously from an global point of view to come and score your first goal and in the second game get a massive assist for us was huge".
"We have quality and now we have to use this quality consistently, that should be the plan", said Klopp.
Wood, who had scored two goals in two games for Burnley, grabbed himself an assist in a 1-1 draw with Champions League club Liverpool on Saturday (Sunday NZ Time).
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Burnley, who could even have poached a late victor through Ben Mee, got an unexpected point to add to the four they secured at Chelsea and Tottenham.
Today's match ended as one of the typically disappointing Liverpool games fans have come to nearly expect against smaller sides such as Burnley.
Philippe Coutinho returned to make his first Premier League appearance of the season after submitting a transfer request in August, but the Barcelona target's numerous wayward efforts summed up the Liverpool's day.
"This one goal, that's where we have to improve most, to switch the mood in being offensive, being offensive - do, do, do all the time - and then this one situation, a little block here and we missed Arfield, or forgot him, and he can score then".
Dominic Solanke had Liverpool's best chance to win the game late on, but his instinctive volley ricocheted off the crossbar, and Jurgen Klopp's men had to settle for a point. Burnley fired a ball into the box and Klavan and Matip both went for the same header.
There is also the issue of extra games this season for Klopp to address and in doing so he will need to rotate certain members of his squad but therein lies a great problem for the German tactician.