Wood, making his first start since the end of January after injury, was twice denied a winner by the impressive Kasper Schmeichel, with the effectiveness of the duo giving Dyche something to think about before Arsenal visit on Saturday.
"I believe in the group, I believe in the four of them as strikers," Dyche said. "There's four decent players there who give a lot for the cause.
"They're all very good players who can adapt and play for us in different ways and that gives us more flexibility."
The combination of Wood's aerial presence and Vydra's pace caused Leicester problems on Wednesday. Asked if he had a best pairing when all four strikers were fit, Dyche said it was about finding the right solutions for different opposition.
"Sometimes you look at the history of a pairing and obviously Woody and Barnesy have been very successful together and have scored goals, sometimes it's about the connection," he said.
"We had a tough decision to make (against Leicester) because we had J-Rod and Vyds, and Woody coming back fit. We protected him a little but on Sunday to see if the extra days helped and then you've got to pick one of the other two.
"They're both performing in different ways and were good at Fulham together. There's the challenge of the schedule at the minute, but if they'd all have been fit they would all have been playing."
Vydra's goal was his first in the league in over a year, a total of 1,212 minutes since he found the net against Bournemouth in February 2020, but the Czech Republic international has had to be patient with most of his appearances coming off the bench.
Six of his seven starts this season have come since the end of January during a time when Barnes and Wood have been out, but Dyche has been happy with the way the 28-year-old has stepped up.
"It was good to see him get a goal and a good goal" he said. "He's been adapting, learning, improving. He's got good energy for the side.
"He's arguably one of the quickest if not the quickest here. He's using that pace and working off the ball better.
"He worked very well with Chris Wood. If we play two up together they've got to come to the party. Both of them gave us energy and looked a threat. I'm pleased for them and for the mentality they brought to the game."
Burnley were 1-0 winners against Arsenal in the reverse fixture in mid-December, taking three points courtesy of a Pierre-Emerick Aubameyang goal at the wrong end after Granit Xhaka had seen red early in the second half.
"The last one doesn't guarantee you the next one," Dyche said. "Especially when you're playing a good side like this with good individuals."